We use an safe deposit envelope in the UK with HSBC. Works fine, but has a 24 hour notice period and you you pay if you take stuff in and out (but inspection is free which is all a bit odd). £25 a year though, which makes it cheap as chips for safe storage of house deeds, etc. For regular access then perhaps not as idea.
Oh, and by envelope, then that's not a little DL envelope, we used a big thick envelope with loads of plans, etc etc. I'd not want to put in a HDD though, as I don't know how it's transported. DVDs would be fine though.