Where is telephone area code 0204?

There is no UK area code of 0204.

London uses the area code of 020 but there are no telephone numbers beginning (020) 4... yet.

If by "0204" you are in fact referring to part of the local phone number after the 020 area code, there are three possibilities:

(020) 3020 4xxx

Issued by phone company Imovo.

(020) 7020 4xxx

Issued by phone company Cable and Wireless.

(020) 8020 4xxx

Issued by phone company Teledesign.

None of these companies make public any more precise location information. The numbers in question could be anywhere in London, inner or outer - or not in London at all, even.