Not wrong
Alas the history of the London phone number is something I know too much about.

First 01 was the dialling code for London.
Numbers were 01 XXX YYYY

In 1990 it was decided that London was too big and the split happened so Inner London became 071 and Outer London 081.
071 XXX YYYY and 081 XXX YYYY

In April 1995 ("PhONEday") these numbers became 0171 and 0181 respectively.
0171 XXX YYYY and 0181 XXX YYYY

In June 1999 (so almost 12 years ago now) London had a single dialling code, and the 7 or 8 was moved across to the second group of numbers, allowing additional numbers in the future
020 7XXX YYYY and 020 8XXX YYYY

Since late April 2000 (almost 11 years ago) the unification was complete and anyone with a London number can ring any other London number (whether it starts with a 7, 8 or even a 3 (or any other numbers that might get added)) without dialling the 020 prefix. It is also worth bearing in mind that this re-unification also now means that there is no geographic importance to the first digit of the local number any more.
(phyphor, Fri 1 Apr 2011, 23:53, Reply)