Would second A3 and Gt Expectations, both really good, just call them to check if they have them in. Also Happicraft in Twickenham, and another alternative is Fiesta Tots in Horsham, they have the Greentom Upp which is a superb pushchair for SN, I've pushed a grown man in it (don't ask!) and I could steer it with one hand, easily the best pushchair I've found for a higher weight.
At 4, you could also speak to Health visitor and ask about a Maclaren major, I had one for my daughter and it lasted her until around 13, when she changed to a wheelchair.
Will let you know if I come across anything else