You'll most likely find that your bank will not allow you to write cheques in currencies other than sterling.....you should check with your bank in case.
You should write the cheque in pounds. The seller's American bank will do the converting for the seller, but it could take 30 days or more for the cheque to clear. You might be waiting quite a while to receive your item, if he/she holds delivery until the cheque clears (which is likely). Just so you're aware!
I have bought from Germany and the USA. My understanding is, if you pay by cheque you are charged a fee to process the change from one currency to another. Because of this I paid by Visa. The card company automatically pay in , say, dollars, and send you a statement as normal converted at the exchange rate at the time of purchase.
I think it extremely unlikely the buy in the uS will accept a GBP cheque, and if they do they will have severe difficulty getting their bank to accept it, and if their bank does, they will have to pay large fee for clearing.
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FYI, Abbey National charge 10GBP to accept a US dollar cheque.