You can look at the English and Welsh civil registration quarters for free at
http://www.ancestry.co.uk/search/rectype/vital/freebmd/bmd.aspxThe civil registration quarter of March 1974 for deaths gives Francis William's death details and also his date of birth.
Francis William Brett 10th July 1918 Coventry (place of death) 9C 1958.
I can't see his birth registration as Francis W Brett in that quarter. If you know the details of his second marriage you can search for the exact reference - quarter, registration district, volume and page number at 'Ancestry' and send for the marriage certificate to find out details of both fathers. GRO website
http://www.gro.gov.uk/gro/content/certificates/If you know any further details of Francis' sister - her married name, when approximately she died, it might be possible to search for her death registration and try to track her birth back (the registration if after 1910 will give mother's maiden name in the index). If that surname was distinctive enough you might be lucky and have it lead you to an marriage on FreeBMD.
FreeBMD is indexing the civil registration index to make it much quicker to search.
http://freebmd.rootsweb.com/cgi/search.plCoverage is good up to about 1910
How good their coverage is is here
http://freebmd.rootsweb.com/progress.shtmlFor births in India - they might be registered in the overseas section of the civil registration either as army births or consular births. The index for those births is on the internet but on a pay as you view website.
http://www.findmypast.com/HomeServletPeople who have credits will do look ups for you. However it is the civil registration index so again you will need to purchase the birth certificate itself from the GRO for further details.
As a longer shot there is a William F. Brett's birth registration in the September quarter of 1918. The details are
William F. Brett
Thanet registration district
Volume 2a
Page 1594
Mother's maiden name Eatwell
There is a potential marriage in the same registration district for the parents on FreeBMD
Marriages Sep 1904
BRETT Benedick George Thanet 2a 2128
Eatwell Charlotte Louisa Thanet 2a 2128
with two other birth registrations for certain to the couple (after 1910 with mother's maiden name) of twins
Births Mar 1914
BRETT Margaret M Eatwell Thanet 2a 1994
BRETT Peter J Eatwell Thanet 2a 1994
Regards
Valda