train from Taunton UK to Heathrow area

Can't help if you're looking for a hotel in a cute little town near Heathrow. For a place right on the airport grounds (covered walkway from Terminal 4), I recommend checking out the newish Premier Inn, which has been offering extremely low rates.

The Sofitel next to Terminal 5 is also very good and convenient, but not cheap. There are many hotels a little farther from the terminals but with good shuttle service, check out the LHR website.

Reading (rhymes with wedding) is a major rail junction with bus service to LHR, but I think it takes so long that you'd be safer staying at or next to the airport than in Reading itself. Slough (rhymes with cow) has a connecting spur to Windsor, with bus service to LHR, or a not-too-expensive cab. Windsor might be a good overnight choice if your flight isn't too early. And of course there's the castle and all that if you want to cram in a little more sightseeing before you fly away.

As you've probably figured out, the trick is to avoid going all the way to Paddington and back to Heathrow. Maybe some of our UK friends will have better advice when they wake up in a few hours.

What time is your flight?

Reading and a bus to Heathrow, or Windsor and a bus or taxi to Heathrow are unlikely to be any faster than staying in the Paddington area and taking the fast and frequent Heathrow Express.

If your flight is too early then it is an airport hotel or a hotel on hotel row and the free bus.

Hotels close to Heathrow don't have courtesy buses so that the traffic around the airport is managed. What they do have is either the 'Hoppa', a paid-for bus that does a route round a few hotels, and/or the regular London buses that in the immediate neighbourhood of Heathrow are free of charge.

How many people are traveling, and what time is your flight from Heathrow?

Those factors will affect your options.