A banker's cheque from your regular UK bank is fine. The US will accept these when the amount is big. The banker's cheque should be in US$$, not in ££.
Most UK banks offer a dollar account. Open one with a few dollars (not the whole shebang!). Then hire a Currency Exchange company to arrange the transfer - argue for 30 basis points or less, no fee, no commission. I can provide a few recommendations offline. The currency exchange will take ££ and convert to $$, depositing it into your $$ account. Your bank will then arrange a banker's cheque for the $$. This will save you $100's of costs from your bank for the joy of paying your taxes.