Re: Wrong dialling code
London's area code is (020) domestically, or "+4420" internationally. The next eight digits are the subscriber number, and the first digit of this has no geographical significance, and there are three ranges in use at present: 7xxx xxxx, 8xxx xxxx and 3xxx xxxx.
The distinction only matters if you're phoning from another fixed line number within London; from a mobile, you always have to dial the destination area code, so it's fine.
The confusion is a legacy of the decade-long manoeuvring of London's phone-numbers in the UK's wholesale reinvention of its numbering plan between 1990 and 2000. From 1990, there were indeed two area codes (071) and (081) which changed to (0171) and (0181) in 1995 before finally being merged back into (020) in 2000.
On "Swap Shop", the (01) 811-8055 number was specially set up for the BBC by the Post Office a year into Swap Shop's run to reduce the number of mis-dials. They picked "811" as it was the most numerically-distant exchange code from existing London exchanges (when entered on a phone-dial). The original "call the BBC" number was (01) 288-8055 [yes, I did have to look that up]. After the 1990 London split, the number became (081) 811 8181, but that was long after my days of getting up early on a Saturday.