I quite like Austin Kaye on the Strand (go towards Covent Garden from Charing Cross) - they have moderns but also an interesting selection of vintage, normally including a few Heuers. Though you would be lucky to see an Enicar.

It's also worth popping into the Burlington Arcade (off of Piccadilly) - shops like David Duggan are more for Rolex and higher end stuff, but occasionally you will find a Heuer amongst them. There are quite a few watch shops along the arcade.

At the far end of the Arcade (if you entered from Piccadilly) is Somlo, which is an Omega-backed shop for vintage Omegas. Even if you're not particularly into Omega, it's worth a look.

Bear in mind at Burlington Arcade, you'd be paying well over the odds to help the shop owners pay their astronomical rents but at least window shopping is free!