There’s a record of a marriage between Edward J Kavanagh & Sidney M B McHugh. They were married in Hammersmith, London. (The details are Oct – Dec 1956, Volume 5c, page 1320). That marriage certificate should give you Sidney’s father’s name and occupation. (Edward is simply the anglicised version of Eamon, but I am sure you probably knew that anyway).
They appear to have had at least one child. Mark Anthony Kavanagh born 12.10.1962 who died in Merton, south London in 2000, aged 37. (Register B43, dist 2441, entry 120). His death certificate should tell you whether he ever married. And the informant might be a relative too.
You will need to order a copy of both certificates to get the relevant information. You can order them from the GRO in Southport, Lancs.
https://www.gro.gov.uk/gro/content/certificates/contact_us.asp
Eamon left a will in the UK, when he died on 10.2.1995. Probate was granted in June 1995 at Ipswich. You can order a copy from the UK wills site for £1.50 (sterling). That will may tell you about any other family he had.
https://probatesearch.service.gov.uk/#wills