Any city with a long and diverse past is bound to produce a strange and wondrous underbelly, though only London would find the biggest belly in the underbelly and elect it mayor. For oddities that don't look like Andy Warhol and curse like a sailor, shop London Peculiar.
Peculiar's an online trove of original capital artefacts ranging from the bizarre to the iconic to the iconically bizarre, searchable by date, price, and location, and all assembled for sale by a dedicated amateur civic historian, a good thing, as professional civic historians would bury all this stuff beyond public view, in, like, a museum.
For your wall, there's a colourful 1800s print depicting a brain mapped by phrenology ("the only true science of the mind"!), a fascinatingly horrific, elaborate poster for the 1827 execution of a wealthy Quaker convicted of the ghastly crime of...forgery, and even a 1st ed, framed album cover for Never Mind The Bollocks, from the band convicted of the ghastly crime of ...letting Sid Vicious touch an instrument.
Object-wise, if you're in the market for a 1930s Metropolitan Police whistle, you're in luck, while there's also treasure waiting for those seeking an early 1900s medical measuring cup, or an original copy of the Savoy Cocktail Book from back when they considered alcohol suitable content for that measuring cup.
For TFL aficionados there are posters including tube maps going back to 1909, Harry Beck's 1933 design, and the '66 World Cup special; if you're hungry for odd historical facts, they've also started a blog ostensibly run by a well-dressed pigeon -- who, considering our current municipal leader's fascination with chicken feed, might just be electable.