'Forest Hill', his birthplace in 1901, is in Lewisham, so the reference that Barbara gives for the birth certificate in Lewisham should be the right one. You can either contact Lewisham registry office directly, or order online at
www.gro.gov.uk to get the certificate.
If he was CoE (you can get some idea of this from which church he was married in), these are the most likely churches he would be baptised in, but you don't need to know the parish to get a birth certificate, just the reference (that's why civil records are easier than parish records).
# Christ Church, Forest Hill (church built 1854; parish created 1855 from [1]) Original registers from 1854.
# St Saviour, Brockley Rise, Forest Hill (parish created 1866 from [12]) Original registers from 1867.
# St Paul, Waldenshaw Rd., Forest Hill (1883-1943 demolished) No Information
There are also these nonconformist churches in Forest Hill:
Baptist, Zion, Malham Rd., Forest Hill
Baptist, Dartmouth Rd., Forest Hill
Congregational, Queens Rd., later Taymount Rise Forest Hill
Presbyterian, St John, Devonshire Rd, Forest Hill
Methodist, Trinity Church New Connexion, Perry Vale, Forest Hill
Methodist, St James, Wastdale Rd, Forest Hill later Stanstead Rd
Methodist, Stansted Road, Forest Hill
Bible Christian, West Kent Park, Forest Hill
Other, Dietrich Bonhoeffer German Evangelical Church, Forest Hill
The birth certificate won't tell you where/when/if he was baptised, but it will give you an address you can use to work out which is the most likely family church.
For his death records, they would be found in seperate indexes as he d. in France. The GRO can supply you with a certificate given the information you already have about when he died, but you should be aware that the record will not give you any more information than you already have.