BACS is a UK only scheme, which is why your bank has never heard of it - i.e. you/they cannot transfer money via BACS from the US to the UK.

Instead you'll need to wire the money via an international transfer - to do so you'll need the recipient's International Bank Account Number (IBAN) and also the SWIFT BIC (a code for the receiving bank) - these will be different from the recipient's regular account number and bank sort code (the latter is used in the UK to identify the branch of the bank where the account is held), so they may need a bit of prodding to divulge the requisite information. You'll probably also need the name and full address of the bank branch where their account is held. Though you probably know all this already!