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I got a refund from some medical treatment in the states. They sent me a US cheque. Can I pay it directly into my UK bank account?
Yes
Yes but you may have to pay for it, costs me £7 per cheque with RBS.
Possibly. Building Societies won't accept dollar cheques, as I discovered with Nationwide. Natwest do, but they charge about £7 per cheque.
If not, find another bank, it's a basic service. Depending on the amount it can be pretty slow, though, because cross-border cheques are a fraud magnet. Check the charges but also check the exchange rate you're offered, some banks will have a terrible cheque rate.
Yes - but see above regarding costs. I get two quarterly dividend cheques from IBM and, luckily, I get free banking.