In my experience London, and cities in general, are not great places to find older generations. Hamleys (Regent Street) is quite expensive, too, though they sometimes have things first. (A lot of buses go to Hamleys and it has its own designated bus stop so it is easy to find. I think by Tube the closest would be Piccadilly Circus, though you'd have to walk a bit). Selfridges is another good one (that's technically Bond Street, I think. If you went by tube, the stop would probably be Bond Street. If by bus, any bus that runs up Oxford St to Marble Arch stops at Selfridges and, again, it has a designated bus stop. And of course, there's always Harrods (Tube stop, Knightsbridge, any buses that go to Knightsbridge stop at Harrods.)
Those are the tourist trap shop options. If you know where your friends are staying/travelling from I can probably give you more accurate bus numbers (buses are cheaper than tubes as the Oyster pass caps out at a lower level. I think it's £4.50ish max price for bus travel no matter how many trips you do, but £6.50 for tubes).
In terms of other G4, the UK stores that stock toys most are ToysRUs, Entertainer, Smyths and such like. Maybe worth checking their websites depending on which part of London your friends are going to. I know there is a TRU in Bayswater, and several others around. Supermarkets can and do have toys here but in my experience the range in London has not been great. I was in Surrey Quays in July and all they had were old stock ponies. In stores here at the moment it's not that exciting, either.
Argos has a lot of exclusives, it's a catalogue store and there are loads all over London. I think they have the ponies Target have as exclusives - I know they also have Trixie, Rarity and Buttonbelle and there was a 2 for £15 offer on there though I don't know if it still is. They have Power Ponies and ManeIac...but if you want a specific pony, you need to say so and ask them to bring up items for you to choose from. Otherwise it's just one supplied from the catalogue number. I think Argos exists across Europe though so you may already be familiar with that one
In terms of second hand it's harder. There's a carboot sale that runs in Hounslow (at the tube station carpark, I forget which Hounslow station off the top of my head) on a Sunday morning but I have only found the odd G3 pony there, no G1 (This was back a few years though). It's a long way out of the centre of the city - almost to the far end of the Piccadilly line on the tube (45 mins?) My only other suggestions are the second hand sales south of the river. I haven't had a chance to go to any myself yet, but I know there's a fair of some kind in, I think, Bermondsey that happens on Fridays and there's some other thing that runs on a Saturday as well. The only thing is that to spot such things means travelling around on buses and hoping for the best, and your friends may not be up for that.
I don't know of many charity shops or second hand shops in central London. Possibly more in the outer zones but again, requires some travelling outside of normal tourist areas.
There may be places in High Street Kensington and other like locations where there is a variety of shops - but I am not totally convinced by this. In the year I lived there I found very little in the way of second hand pony options. I did get Feather May and Honey Buzz from Hamleys, though, and never did see them anywhere else in the UK.