On this magical tour of London, there is only one place to start. That is platform 9 and three quarters, the now famed platform that took Harry and his friends to Hogwarts via the Hogwarts express every year. This continues of course, but given the fame the original platform has now got, it has been moved to a location that changes each year for security reasons.
Aside from the walled entrance to the platform, there is also a shop here, where muggles, witches and wizards alike may buy supplies needed for any eventuality. I am unsure if they accept money from Gringots, but they do accept muggle money.
Next door to Kings Cross is a new exhibition revealing how Harry Potter is actually real. The British Library had to work very closely with the Ministry of Magic to approve the contents of the exhibition so that it was balanced between giving some secrets away to satisfy the muggles, but not enough to completely destroy the statute of secrecy that the wizarding world values so dearly.
After exploring these two areas where magic and muggle collide, it is now time to get on muggle transport, either the underground railway, known to muggles as the tube, or the muggle bus, which unlike the knight bus is red and does not bend.
The destination is Oxford Street, more specifically the part of Oxford Street that is next to Tottenham Court road, which some sensible muggle also used to name the local tube station. Here, if you look closely enough you will find the Diagon Alley outlet shopping centre, known to the muggles as primark. If you are eligible to enter via the witches and wizards entrance, the window display will indicate when you are able to enter. For all others, please use the muggle doors. In this shop you will find all manner of useful items for all your wizarding needs, at greatly reduced prices. For your convenience all the shopkeepers at Diagon Alley have agreed to put their items in the one outlet shop, in the spirit of wizardly co-operation.
A short walk from the outlet shopping centre you will find an exhibition put on by famed illustrators in a shop they called after themselves "the house of Mina Lima". In this you will find all manner of items to both look at and purchase to add a bit of magic to your walls. Although the illustrators of the daily prophet are a closely guarded secret, it does appear to be a very similar style to these fine portraits. If you are a muggle, the images will not unfortunately move for you.
A short walk from this location is the muggle bus stop to what the Muggles like to call Victoria Coach Station. If you have the correct ticket though you will also find this is the central location of the Knight bus, given the recent heightened security after too many muggles successfully hailed the bus using their wand arm, leading to confusion from them, the people on the bus and its driver and conductor.
Perfect for a day out. Here is a simple map of the locations in Muggle London.