There are other systems that are also used in London.
European elections use a party list in a multi-member constituency.

For the GLA we get two votes, so it is not a simple closed party list system but the Additional Member system.

And it is not entirely right to suggest that FPTP is used for local council elections, these use Plurality-at-large.

Personally I particularly dislike the method for electing the Lewisham Mayor, where we have only two votes - we should be able to number every candidate to ensure we have our say in the second round. In the 2010 election approximately 18,000 people did not use their 2nd preferences (17% of voters) and another 4% of voters failed to complete the paper correctly and their votes were regarded as invalid (some of these will have been intentional).

It is time that we found a way to computerise the entire process so that voters are warned when they do not correctly cast a vote, with the additional option of registering a protest vote against all the candidates.