There are lots of numbers associated with bank transfers - I'll try and go through some of them here.
Sort Code - Unique identification number for a particular bank or building society branch. For BACS processing this must be a six digit number, however it can be represented as three two-digit numbers separated by dashes.
IBAN - International Bank Account Number (IBAN)
IBAN is an initiative being driven by the European Commission and banks across Europe to introduce a standard account number format for use with cross border payments in Europe.
Example of a UK IBAN:
Country Code Check Digits Bank Code Sort Code Account No. GB 99 RBOS 123456 12345678
Society for Worldwide Interbank Financial Telecommunication code - this number is generally used for transfers between the UK and the US
So it really depends on where you are as to which numbers they are going to need from you.