"Budget up to around £10k

I live in London and tired of hiding the watch under the sleeve, so needs to be able to wear with a T shirt in summer without being worried of theft

Not Rolex due to above, or anything that can be mistaken for a Rolex"



That will be tough because many thieves know their watches I would imagine, not just Rolex and obvious ones.

If that is a real priority then I would get a PVD or DLC coated watch, they blend in much better with the Borg wearing all types of black looking watches.