UK bank account numbers is a 6 digit sort code + 8 digits account number. The account number is unique for the bank, and assigned however the bank wants. It might very well have been sequentially assigned for some institutions.
The 6 digit sort code is unique for the bank branch across all UK banks, generally the branch on record for the account (most UK banks use the sort-code for the branch the account was opened at). Unless you happen to mistakenly enter an account number and sort-code that matches, and you manage to mistakenly enter the name of the account holder for that bank account, they'll usually catch it.
The situation is similar across Europe, so if this is a problem in the US, it's a problem of the banks own making, and one easily solved the same way it was in the UK: By adding a sort-code, and matching on the name as well.