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the USA extended warranty does not apply to UK cars. BMW UK may consider replacing the pump under goodwill, however (depends on mileage, and in service date and if they are willing to help or not)
this should be carried out by a BMW main dealer or BMW specialist shop. for goodwill, it will have to be a dealer
you are looking at about £200 plus 3 hours labour to replace.
Sorry if you were hoping for a different answer, please don't shoot the messenger - I can only give the honest answer, which I have. Please remember that a low rating PUNISHES me for my honest and prompt response, and I receive nothing for my time and answer until a positive rating is clicked.Please let me know if you have further questions. Please do not forget to click a positive rating as this is the only way I receive credit for my answer, thank you. Best wishes with your vehicle.