I had no idea my 'simple' question would arouse such a flood of responses. Thank you, everyone.
Unfortunately, no-one in the family in Australia knows the facts other than what I'm stating here. Philip had an only sibling, a brother in the RAAF who was injured in WW2 and had no children, and his unmarried uncle in the Australian artillery was killed on the Western Front in WW1. His aunt (my grandmother) was the only sister of Dr Nigel Boulton, who was a doctor in the RAMC in WW1. My mother, in her 90s, remembers only that her cousin Philip supposedly had a son and my mother also 'thinks' that Eileen died young, which is Mum's reason for why the family lost contact. It may not be true.
There was no child before Philip's marriage, as he did not arrive in England until June 1939 and he met Eileen soon afterwards. Philip wrote a letter to his father at the time of his marriage in January 1940, saying there were no plans for children until the war was over, but further letters from him have not survived. 'Accidents happen', so Eileen could well have had a child before or just after he was killed (29 May 1941). She was working in the Auxiliary Territorial Service when they married.
The family in Australia would have been strangers to her and she probably felt her duty was done in sending the few photos that we have here. There is a photo of a child aged about two, while the child in the photo taken at Alperton Cemetery looks to be about six years of age. The photos are undated and unidentified, except for a later annotation 'Philip's son'.
Just to reassure anyone reading this topic, in past years I've looked everywhere I can think of without actually spending any money on BDM certificates of possibe relevance to Eileen. I've now concluded that the most important piece of data at this stage would be to find her exact date of birth, so that I can narrow down the options for her death under various possible surnames.
When I started this topic earlier today, a number of messages ago, I was pretty sure she must have been the Eileen M Sellars whose birth was registered at Driffield in the Dec Qtr of 1920. From everyone's feedback, I realise that I should forget about finding the baptism and instead I should purchase the 1920 Driffield cert and also the 1922 Hammersmith cert.
Thank you, everyone, for your help.
PS Thanks for the search in Scotland but there has never been any mention of a Scottish connection.
PPS Before i close, I'm wondering how to get a copy of the will for the 2007 death of Eileen Mary Saben, should I discover that I need that. The will would presumably state at least one family member.