Re: just like the phone numbers
London was changed to 01 xxx yyyyy to 071 xxxx yyyyy so that all other land-lines could be changed later from 0 aaa bbbb to 01 aaa bbbbb. At this time, London could then change from 071 to 0171 or (as it happens) to 0207.
Doing London from 01 to 0207 at the same time as the '1' was being added would be a recipe for confusion, as it would be difficult to tell if '01' was the correct new code for an number, or someone using the old London code.
Now, all numbers starting 01 or 02 are to landlines; the second digit of the phone number will give you an idea of what type of number you are calling (although it is not perfect)