Ann Marie,
Take a look at Citi Bank. They will allow you to open a dollar account into which you can pay dollar cheques free of bank charges. If you ask for a paying book and pre-paid envelopes, you can put your cheque in the post when it arrives and it's easy peesy. I just sent off my first Amazon.com cheque myself.
At the same time, you will need to open a Citi Bank account in sterling (pounds). You can then transfer your dollar balance into your Citi Bank sterling account and you will have your monies in sterling without being charged any fees. You can then take out the money in the usual way - it's probably easiest to do an electronic transfer into your regular bank account.
There are no charges for this account, but you will need to go into a branch to set one up. Even if you live a long way away, it's the only way to do it. They will sit you down and talk to you about your finances (in the hope, I think, of making money out of you), but when they realised I had no money to speak of, they happily set me up with just the dollar and sterling accounts and off I went. These can be managed online and you don't need to go into the branch again.
Make sure you phone ahead and make an appointment - if you pop in on the off-chance, they may not be able to see you (this happened to me).
I took this action after a long internet search. Please do not use any online company that offers to transfer your money electronically for you - I've read a lot about people who've done this and never seen their money.
You also mentioned that you're paying tax. There really is no need to pay tax to the American government (IRS) if you're a British citizen. But you'll need to go through some hoops to do it. You will need an ITIN (a tax number which tells the IRS you're British and not to tax you). To get this, you will need to fill in a form called a W7. When you have your ITIN, you use it to fill in a W8 which you send to Amazon (& whoever else, eg, Smashwords).
The whole ITIN thing is a right pain. Go to the Smashwords FAQ and read up all about it - theirs is the most helpful site (I've found). They will also send you a letter to accompany your W7 if you've earned a minimum of $10 on their site (not earned it? Buy $10 of your own books!). Amazon Kindle direct has a helpful copy of a form showing how to fill it in (if you search hard enough).
(I've read Amazon can also send out these letters, but Smashwords is simply more user-friendly)
You must - and I cannot stress this enough - take your completed W7 form to the American Embassy with your passport to verify your identity and get them to send it to the IRS on your behalf.
Even if you live in the wilds of Northumberland or the tip of Cornwall, you must go to the embassy. I tried doing it through a solicitor, it cost me £60 and I got rejected (the man at the embassy said only solicitors in the US are qualified to do this).
Until then, adjust your Amazon account so you do not receive revenues until you have a high amount in your account (eg, $500). Once Amazon has accepted your ITIN, you can drop it to $100 again and get your cheques - tax free! (Of course, you must still declare you income and pay UK tax!)
There's an option on Smashwords to withhold your money until your ITIN is sorted.
I've read of some high earners who didn't bother with the Citi Bank account and see the bank charges for cashing foreign cheques as part of their business costs. But they also made sure they didn't get a cheque lower than $500, so it wasn't such a big hit.
It took me many months to learn all this. I hope my advice is of help.
