So the question is what to put for foreign tax paid on the US return ? Do I make an estimate of what HMRC will take?
I can appreciate the OP's point and it has always puzzled me. Even after seeing how a professional prepares a US return, I remain rather perplexed.
Suppose, for example, one has a newly opened UK bank account that pays its first annual interest, say £1,000, on 1 December 2015. Logically, one should record this on the 2015 1040 and take a foreign tax credit for the 20% UK tax which has been deducted at source by the bank. If the tax payer has UK marginal rate of 40%, and UK Self-assessment is then completed promptly, say in mid April 2016, then there will be a further 20% UK tax computed on this interest, but this is only a "tax accrued," and need not be paid until 31 January 2017. So should a tax credit to be taken on the 2016 1040 (if UK tax is paid in April 2016) or on the 2017 1040 (if paid 31/01/17), or can - as the OP suggests - this be taken as a credit on the 2015 1040, "by estimating"? I suppose that by paying the UK tax earlier than required, say May 15, then it can be marked down as paid on the 2015 1040 which you are going to file by June 15. I appreciate that there exist tax credit carry forward provisions, that can smooth this problem once the OP has been paying UK tax for a few years and has built up credits in all 1116 baskets, but the OP says this is the first year that he or she is back in the UK.
To complicate things further, there may have been a payment to HMRC made "on account" in January 2015 for tax that will be due for UK tax year 2015-16. Payments will be made 31/01/15 and 31/07/15. but it is hard to disentangle what part of the "on account" payment is for the higher rate tax that HMRC is estimating will be owed on the bank interest (if income were to turn out to be the same), and should this be taken as a credit on the 2015, or 2016, 1040?
On top of all this there is the wrinkle that for the 40% marginal rate UK tax payer, tax on wages and bank interest both flow to Form 1116 (general basket). Suppose that in 2015-16 UK tax year someone has £10600+21785 wages and £15000 interest. She will pay 20% on the basic rate amount of 31785, and 40% on 5000. But what part of this is tax on wages and what part is tax on interest? Is the UK tax charge on wages 20% x 21785, and on interest 20% x 10000 + 40% x 5000? Or should the total tax be allocated between them proportionally? Does the interest now go on 1116 general or passive?