The current standard is ISO 13616:2007, which indicates SWIFT as the formal registrar.
Many European countries use the IBAN as a means of identifying bank account numbers, but transfers to, amongst others, the United States and Australia make use of the BIC Codes. The Sort Code Checker uses the latest industry data, which is updated weekly, in line with industry practice.
The underlying rules for IBANs is that the account-servicing financial institution should issue an IBAN, as there are a number of areas where different IBANs could be generated from the same account and branch numbers that would satisfy the generic IBAN validation rules.