I'm afraid that before civil registration began on 1 July 1837 there is no such thing as a birth certificate. You need to look for a baptism in the parish records. The IGI is a good place to start:
http://www.familysearch.orgIt is NOT complete.
It might help if you knew which part of Middlesex he was born in. Have you found him on any census e.g. 1851? This usually gives more specific places than just the county name.
Depending on which part of Middlesex the original registers are kept in London Metropolitan Archives, Guildhall Library, Westminster City Archives or a couple of other places for a small number of parishes.
Have a look at the GENUKI site:
http://www.genuki.org.ukAsk if you need anything else.

Nell