What branch of Santander has the sort code 09 01 25?

There is no bank, Santander or otherwise, with the sort code of 09-01-25.

The nearest, numerically speaking, sort codes belonging to Santander are: 09-01-18 which is the branch based at 21 Prescot Street, London, E1 8AD, England; and 09-01-26 which is the Santander located at P.O. Box 382, 21 Prescot St, E1 8AD, London, England.

Santander Took Over Many Banks During the Early 2000s

Building societies such as Abbey National and Bradford & Bingley were subsumed into Santander, and by 2010 all former branches of these societies were renamed Santander. Perhaps the bank you had in mind was closed as a result of these changes.

What is a Sort Code?

A sort code is used by British banks to direct route money
transfers between themselves via their own clearance organisations.The sort code is usually three pairs
of numbers, e.g., 54-21-06. This identifies both the bank and branch. You can
often tell which bank the code relates to by the first two digits; in this case
of ’09,’ this indicates a branch of Santander. Six-digit
sort codes were brought in during the 1960s as banking increasingly relied on
computerization, making banks easier to identify themselves and each other. 

Here's a famous face advertising the old Abbey National back in the late 1980s: