Paxboy
The London taxi is regulated by either TFL or the Public Carriage Office (formerly a Met Police branch). All taxi's are licensed and all fares will be on the meter from the point of departure, (not starting at the taxi rank outside as a little fiddle in the past). All points of arrival within the GLA or TFL area are on the meter. No taxi driver should show you a price list. If outside the above areas then it is by agreement, and it is unlikely the taxi will take you.
The driver should not refuse taking you to anywhere within the GLA area.
By example a few years ago before Staines was expelled from GLA/MPD the driver said no, I said yes it is still in London = bad luck. They always want the big fare to Central London.
Hope this helps and is not out of date or critical of taxi's. The TFL website is best.
http://www.tfl.gov.uk/modes/taxis-and-minicabs/
T09L