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For aught I know, Cambridge and Oxford don’t accept SAT scores. And I doubt that such elite schools as LSE&Warwick will accept SATs.
Shanghai has many great international schools which offer A-Level courses and tests. You may contact school counselors and see if they could let you take A-Level tests at their schools. (Usually, however, these schools don’t accept test registrations of students from other schools)
I have a little confusion about this sentence :
Do you mean that you are an undergraduate already? trying to transfer to UK/US colleges? Then I don’t see that SATs can help in applying to British universities. (Maybe for US colleges) You’d better email admission officers, as suggested by peachaso.</p>