The quickest way is likely to be bank-to-bank, particularly if it's a large amount. Your family member will need:
Name(s) on account,
name/address of bank,
Sort-Code,
AC number,
IBAN number,
BIC number
If the IBAN and/or BIC info is not on the transfer request, it could 'bounce' or go astray. I've initiated a transfer and US$ was in my UK account that same day. Your bank/family member's bank may have differing requirements or timing.