It’s incredibly uncommon for drug testing to occur in most jobs in the UK, let alone for internships. The only places it would be considered would be safety-critical jobs. Also, the number of false-positives due to medications etc make drug tests not only an infringement on our civil liberties, but incredibly inaccurate.
You should have no problem in the finance sector as drug testing is near unheard of. One of my friends’ bosses even smokes the stuff, so I think you’ll be pleasantly surprised.
If you EVER are asked to submit for a drugs test (although I highly, highly (pun not intended) doubt it), reject it on the basis of civil rights. We have numerous laws and legislations in the UK to protect worker’s rights and I’m pretty sure this would be covered.
Hope that helps!