It's easy to visit the major wine regions of Germany from Britain, and you can usually get by pretty well with little or no knowledge of German.
By plane, Ryanair run several flights a day from Stansted near London to Hahn airport (which they call Frankfurt-Hahn, despite the fact it's a long way from Frankfurt....), and although this is a rather poor airline with unsavoury business practices, and not exactly cheap, it can be very convenient, especially for the Middle Mosel. There are also flights from Birmingham, Manchester, Glasgow, and Edinburgh. There are also flights from many other European countries, and a few non-European countries. See Ryanair's wesbsite for more details. A few other airlines also use this airport - see the airport website. Unfortunately, this is my recommended method of getting there for visiting the Mosel-Saar-Ruwer, and for the Rheingau, Nahe, Rheinhessen, and Rheinpfalz you have a choice of Hahn or Frankfurt airports, with Köln-Bonn a better alternative for the Ahr. There are fairly regular coaches from Hahn to get you to most major destinations except the middle-Mosel, which is close enough to do by taxi, though hardly cheap. There are also a few mini-buses daily. See the airport website at www.hahn-airport.de for details of coaches, mini-buses, and taxis. For Trier, you can try Luxembourg airport, which is closer than Hahn, and there's a mini-bus service to get you from the airport to the city, though I haven't yet tried this route. The Deutsche Bahn website can be very useful for planning onward journeys from Frankfurt or Köln-Bonn airports, or see here. From Frankfurt Airport there are train connections to Wiesbaden (Rheingau), Mainz and Bingen (Rheinhessen) Würzburg (Franconia), Koblenz (Mosel) Boppard (Mittelrhein) and Bad Kreuznach (Nahe).

I can't really offer advice on getting there by car as I've never done it, but since the major wine regions are in the west of Germany, it shouldn't be too difficult provided you're confident about driving in Europe. Travelling by car, or hiring a car in Germany certainly has it's benefits, enabling you to visit many towns and villages as you please, without having to use public transport. That said, public transport is mostly pretty good in Germany, though there are a few major wine villages on the Mosel that are barely served by bus, including Ürzig. One or two buses occasionally make a detour through Ürzig, but details are sketchy. Thankfully it's within walking distance of Zeltingen and Erden, though it's a fairly long but mostly very pleasant walk of around 45 minutes each way from Zeltingen, the exception being part of the way where there is little or no pavement. However it's mostly not too bad, and the scenery is often stunning. In general, the region from Trier to Traben-Trarbach seems to be fairly well served by buses, and the part from Bernkastel to Traben-Trarbach also has a good river-boat service (summer only) that offers stunning views of the river and vineyards. The boats also routinely stop at Zeltingen, and sometimes also other villages such as Graach, Wehlen, and the first boat company listed below also stops at Ürzig, but they only seem to stop at these villages on request. There are also a number of other river-boat services operating on routes such as Bernkastel to Trier, but some of these are only once a week. Check the websites listed below for details. One aspect of buses on the Mosel that you need to know, however, is that although they run to a timetable they're often 5-20 minutes late. If a scheduled bus doesn't turn up on time just wait; I've never had one not arrive at all. I've put all the information I have about buses on the Mosel on a separate page here.

You rarely need to book a hotel in advance unless you want to stay in one of the main tourist villages such as Bernkastel in high season - there are many guest-houses available to passing visitors in most of the wine villages, most of them with a small winery attached. This makes it very possible to spend a day or two in each of several villages, making up your itinerary as you go. If you really want to book in advance, however, virtually every wine village has a website. Just type in www.piesport.de, or www.zeltingen-rachtig.de, or www.bernkastel-kues.de, www.traben-trabach.de et al. These websites are usually run by the local tourist office, and you can sometimes book hotels directly from these websites, or they will provide a list of hotel websites or email addresses. However remember that where a German word uses an umlaut (two dots above a letter) that letter usually has an 'e' added after it in web addresses. Kröv thus becomes www.kroev.de. If traveling in a group of four or more, you may like to stay in what they call a 'Fereinhaus', which is basically a self-catering flat or house, and which many wineries offer. These probably need to be booked in advance, especially in high season. Of course, if you want 3-star or better accomodation then you should always book in advance. If you should get stuck without accomodation, however, just visit the local tourist office who are always very helpful. If you can't speak German you can always count the number of nights you need on the fingers of your hand.... Here's a list of all the tourist offices on the Mosel that I know of.

One activity on the Mosel that you might like is walking through the vineyards, which is not as foolhardy as it sounds. Many of the best vinyards are steep, and some are exceptionally steep, so over the years the German Govt. has improved conditions for those who work on these slopes by cutting small roads into the hillsides, and of course visitors are welcome to use them too, gaining safe and easy access to beautiful sights that were formerly only available to very sure-footed climbers. Some of these little roads can be seen in a few of the pictures on this website - see here. Most of the winemakers will offer advice on safe, interesting, and fairly easy walks through the vineyards, or if you see a small road leading off into a vineyard just try it, making sure you can remember the way back, of course - some of them are dead-ends, with no exit other than the way you came in. One thing I would advise if walking through the vineyards, however, is taking an umbrella with you, as the weather on the Mosel can be rather changeable at times, and it may take quite a while to get back to a village. As well as the roads, there are also many tiny paths, some of which can only be recommended to those with good hiking shoes, a head for heights and a good sense of balance. There are also many cycle paths along the river which walkers can also use, but do try to give the cyclists plenty of room - there are many groups of cyclists in summer, and the cyclists have right-of-way. I believe that it is possible to hire cycles in some wine villages if you wish - ask at the local tourism office, or at your hotel.

If visiting Trier I strongly recommend a visit to the Trier Landesmuseum, which has a stunning collection of Roman artefacts, including the Roman wineship gravestone, the Diatretglas, a glass which is surrounded by delicate glass netting, a vast collection of mosaics, and the largest collection of Roman gold coins anywhere. This is said to be the finest collection of Roman artefacts north of the Alps, which I can readily believe. Trier also has many large-scale Roman ruins, such as the Kaiserthermen, a hot baths; a Roman amphitheatre where unfortunate Christians often met their end; and the Porta Nigra, a Roman city gate built in AD 180.

If you only want to buy wine in Bernkastel, it's easily possible to just make a day-trip from London, and you can spend six or eight hours there if you wish. I have done this on many occasions, though recent restrictions on hand-luggage mean that this is not all that viable an option - Ryanair has a miserly 15 KG luggage limit, and excess baggage charges are high. You can also reach nearby villages such as Piesport, Graach, Wehlen, and Zeltingen by public transport, but if you want to meet any wine-makers it's obviously best to make an appointment in advance. While I am not very keen on the Gault-Millau 'Guide to German Wines' book (available from Amazon), it has the details for numerous fine German wine estates, including web addresses, email, etc.

It's both disheartening and very messy if you have a bottle break in your luggage, so IF BRINGING WINE BACK TO BRITAIN BY AIR I MUST RECOMMEND USING LOTS OF BUBBLE-WRAP! Preferably also use several large soft towels as further cushioning. Obviously I recommend suitcases on wheels if this is what you're planning, and preferably strong ones at that.

Here's some links to websites you may find useful.
Ryanair
Hahn Airport
Deutsche Bahn (Trains, and also some buses; this website has an English section)
AirportLiner to Trier
Riverboats 1
Riverboats 2
Riverboats 3
Trier information
Trier Landesmuseum
Mosellandtouristik (Books, maps, tourist info, organised tours, etc.)
Mosella (online info for almost all the villages on the Mosel, including many tourist offices)
Moselbahn (Buses. Particularly useful information on route 333, which runs in sections from Trier right the way through to Bullay. Click on 'Fahrplan'.
RMV. Another bus company, this one runs the route 300, from Wittlich train station to Bernkastel via Zeltingen. Again, click on 'Fahrplan'.