You can find several duty watches in Portsmouth Naval Base but get one that's duty free if you can. A Rolex Submariner that shows in a dim light, particularly one with large hands, would be good (there's a few on this forum) but any Rolex Oyster Perpetual should do. Just make sure it's got a dark non-reflecting face or a dial cover.
Personally, I'd buy a hundred Casios for the same price then it won't matter if you lose or break the odd one.
How far along in the recruitment process are you?
Passed all tests and PRMC or just got the brochure and/or had a look on the website?
I'd wait until you've passed out before you buy a real Gucci bit of kit, a bog standard G Shock or similar would see you through training and give you a chance to get something better later on.
Don't bother buying one. When you join CTC, they remove your brain. When you get your green lid, your CO will ask you if you want your brain back or a chunky watch. Anyone who asks for their brain loses the green lid and is escorted off the premises.