The Wellcome Collection is a free museum and library, mostly dealing with medecine and social history. The exhibitions are unusual and engaging, and the permanent collection includes bizarre items such as medieval masks and human remains.

Leila McAlister's grocery shop and café off Arnold Circus, Shoreditch. You can find the best of everything, from jars of horseradish to eggs and croissants.

Eccentric and surprising house and museum of architect Sir John Soane. Mostly unchanged since his death over 180 years ago, it is full of atmosphere. Also have spotlit, late night openings.  

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An obvious choice but no 'best of London' list is complete without the Barbican