Get her the biggest, most shiny ring you can get and is appropriate to her tastes. Just because she doesn't wear jewellery doesn't mean she won't want an engagement ring!
This +1 - engagement rings are special to a girl, if you can find one to her taste, then go for it.
I couldn't find one I liked, so I proposed with a fake costume ring, and she still has it as it is special and wore it every day until the ring we had made up arrived and then it went into a special box for safekeeping.
Most girls will compare rings, and if she is as serious as you are about the whole thing, a ring will mean a lot to her even if she doesn't wear rings normally as it is an engagement ring.
Most jewellers in Hatton Garden are OK, they key is to haggle and maybe go for a less than perfect clarity to keep the cost down, it won't be noticeable in real life. They cater for all budgets, all the rings in the windows cost thousands, don't be put off, go inside and give them a budget and they will work to it as they all want your business.
Take some effort on the proposal, do it somewhere that means something to you both, and well done for sorting it with the parents first, her dad will forever like you for that, too few people do it now
