Despite some of the answers you've received, there is *no such area code* as 0207 or 0208.
The area code for London is 020.
The rest of the number is either 8xxx xxxx or 7xxx xxxx.
You can tell this by trying to dial one London number from another. Even if your number starts with 8, you *still need to dial the 8* for another number within the 'outer zone'.
And conversely, if you're on an 8 number and you want to dial one in 7, you *don't* need to dial 0207: you can just dial 7.
Try it, honestly.
Anyway, to answer the question, there are two main styles of numbers in the UK. Most geographical numbers are in the format:
01234 123456
However, larger cities (Birmingham, Manchester, Liverpool, Glasgow) are in the format:
0151 123 4567
And London, as I mentioned above, is in the format:
020 8888 8888
Mobile numbers all start with 07:
07123 456789