Banking question

[gritsinmisery]

Banks have vaults with locked boxes for their customers to let rent, to store valuables.  Typically one keeps very important documents like birth certificates, passports, stock certificates, etc. and perhaps very valuable jewelry or other items one only uses once in a very great while.  In the States we call these "safety deposit boxes."  I never dealt with the British ones when we lived over there, because as foreign citizens it was kinda important to keep our passports close to hand in case of emergencies.

I would like to know the Brit-speak for these boxes, please.