If you want a peaceful day out of the busy city, Highgate doesn't really feel like London. The cemetery is interesting and peaceful, there's a tour of the old half which is definitely worth the money. Karl Marx, among others are buried there.
I spent a lot of time in the British Museum whilst studying for my Degree. My work has changed considerably since then but it is still a place I return to again and again. Inspiration doesn't always come from objects in the collection but also from the space and its visitors.
One of the main sources of inspiration for my work are unusual objects, vintage toys and tools. A great place to find them is this genuine car boot sale, which is clear of 'bargain' toilet paper and questionable cosmetics. Another plus are the comparatively sociable opening hours. (it starts at noon… )
A walled secret garden, the Physic Garden is like a time capsule, founded in 1673 to allow apprentices of the Worshipful Society of Apothecaries of London to study the healing properties of plants, it is now a living museum. Tours are offered by volunteers with immense knowledge of botany and the cultural history of the garden or visitors can wander the grounds alone and spot odd and fascinating plants such as the mystical Mandrake.