It's also within walking distance of the London Transport Museum. However, I don't visit the LTM these days - it got ridiculously expensive when they did away with 1 day admission and made everyone buy "annual admission" tickets instead, at quite a few times the (already high) daily rate.
As Chris said, but Sidcup is still in London! It is just a suburb. … Charing Cross is a station right next to Trafalgar Square.
I am not sure about Sidcup being in London - I always thought it was in Kent - but I certainly wouldn't start an argument over it.
All I know is that it's covered by PAYG Oysters - and certain Travelcard zones. It's also quite a pleasant (and not too long) journey out to Sidcup. When you get there, you walk down the ramp at the road bridge end of the station - turn right - and Invicta are a few metres along on your right.
I can also add that I've found the people at Invicta a real pleasure to deal with.
As for Jane's Trains (a few doors along from Tooting railway station), I like them as well - however their main stock in trade seems to be secondhand (of which they generally seem to have a good, changing, selection).
I'd agree with other people here - if you are after model shops, central London seems to be very much of a desert. The only other model shop in London that I tend to have much to do with is 4D (just off Leman St.) - but they mainly cater for architectural modelmakers, so they are mainly about raw materials (especially ones that nobody else seems to stock), so unlikely to be what you are looking for.
Edited by Huw Griffiths, 13 June 2018 - 16:17 .