If I (freelance uk resident) get paid for remote work from the US into my US account, will I pay taxes in both countries?

For the years that you were in the US, did you file tax returns in the US and back home? If yes, you are in a good position. Get good tax advice for both counties and file returns for both countries while you have income from abroad. Depending on details, you may still have to pay US taxes even if you are outside the US.

If you did not file a tax return for each year, then you need professional advice. I would not worry about bank fees, I would worry about a tax lien. If that happens the US company would not be able to pay you at all (actually they would send the money to the IRS). Moving the payments to a bank outside the US would not help in this case but instead make it easier to collect from you and possibly charge you with tax evasion (again get professional advice ...).

If you did everything correctly regard tax returns, then I would just ask the US bank for debit and credit cards plus checks. Speak to your local banker and just make regular check deposits into your account. Your banker can probably waive all fees if this is a recurring transaction. They will want your money in their bank and not in a US bank.

Contact an accountant with experience in both countries. Getting this wrong could be expensive.

While you are still a US person (i.e. at least to the end of this tax year), you do not want to be self-employed and overseas. The ~13% employers contribution to social security and Medicare taxes are not covered by reciprocal taxation agreements or by the foreign earned income exclusion.

Responding to @Neuromancer's comment: for the next tax year, you should register for VAT, as your work in the USA does not need VAT added (it's an export), but you can still claim back the VAT on your home office expenses.

As to the cost of wire transfers, it should be pretty negligible on the scale of a bill from a professional you're willing to hire from another country. Agree to roll over your billing until the wire transfer fee is %1 of what's owed, and then bill them.