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There is a "totalization agreement" between the United States and the United Kingdom for Social Security benefits. Social Security suggest you contact.
Or you can apply for US benefits at any UK benefits office.
You will need, at least, your U.S. and U.K. Social Security numbers, proof of age for all claimants, and information about the worker's coverage under the U.K. system.
You are correct that UK coverage can be used to cover the required 40 credits if you have at least 6 US credits, and US coverage can be used in the UK to cover the "basic pension", if you have at least one year of UK coverage.
I'm going to be offline for quite a while, probably at least 12 hours. If you need more information, and that is not acceptable, please "opt" me out. I won't be offended.