I haven't found anything similar with London. There are ones showing the layout of the whole of London in Roman times or medieval times, which don't really give a sense of what it was like at street level, and there are models of individual buildings. There are a few models of old London Bridge that kind of show you what it was like at street level, as old London Bridge was essentially a street going over the Thames. The Museum of London at Docklands has a model which is split into two sides - London Bridge 1450 and London Bridge 1600. My favourite model of London Bridge though is in St. Magnus Martyr church, the church that was actually at the north end of old London Bridge. It may be a bit scrappier than the Museum of London model, but has plenty of character.
Museum of London model
St Magnus Martyr Church
Based on these wonderful models, I thought I'd try my hands at building a model of London Bridge too, just as something to keep me occupied in the evenings. Unfortunately, I don't really have the space for a proper model or proper model making tools, so I had to build it on my computer. It's meant to be how it was in 1550.
