Where can I stash a rental car while visiting London?

To start with probably you want to avoid the Congestion Charge Zone (you have to pay to drive in the centre on London).

The easiest way would probably be to book a hotel with a parking space included (but possibly the most expensive). Otherwise you can find various parking options using http://www.parkopedia.co.uk/. Depending on your preferences, you can find a proper paid car park, or leave the car in a street, somewhere where parking restrictions do not apply during your stay. Parking restrictions are detailed on parking signs next to the road. If there are no signs and no lines next to the pavement then there are no restrictions and you can leave your car there.

When I lived in South West London, which may work for you, Putney Heath was very popular with the commuters. There's no street parking permits required down many roads around it, and then once you've parked, it's a 15 min walk down to the Putney Overground Station, or 20 to the East Putney District line Tube station.

Regardless, make sure you're aware of:

• the congestion zone. You definitely want to be outside of that.
• street parking permits. They're usually labelled pretty well, but some areas look like sweet parking, until you realise everyone has a permit. And they check, frequently.
• some pubs have overnight parking, which is worth looking out for.
• as someone else mentioned, consider just returning it to say, one of the rental companies in Putney Bridge (I used to rent cars around there), and picking up a new rental when you leave - as it's easy access out to the A3 from there, and very close to public transport.

Consider dropping the hire car off and picking up a fresh one when you're done! Most car hire will let you do this for a modest fee (normally around £25-£75) depending on where you're attempting to drop off to...