Once upon a time, every bank had a proprietary trading team in London. Now prop traders in banks are as common as LibDem MPs in England. However, one last bank maintains a prop trading operation and shouts about it.
That bank is...Santander.
Anyone skeptical of Santander's prop credentials is advised to visit this webpage, reproduced below.
Conclusion: Santander prop trades and it's proud of it. Recruiters say the bank's prop team is "small" however and the bank claimed its prop trading activities were "negligible" as long ago as 2010. However, do seem to be some self-professed prop traders knocking around at the bank. Try Alejandro Baño, head of prop trading at the bank, Alvaro Shea, a prop trader with 15 years' experience, or Alfredo Fernandez, a prop trader at Santander for 19 years.
It's no coincidence that Santander's senior prop traders are Spanish: they're all based in Madrid. However, the page above suggests there may be a handful hiding in London too.