I think I was not the only one confused by this! --
"Webber family or descendants of Leonard Webber"
... since if he had no children, he had no descendants. I've figured out that you must mean "Webber family or descendants
of the family of Leonard Webber" -- ?
If his mother Lucy Webber is the Lucy Veale whose death was registered in Devon Central in 1972, her date of birth was 21 April 1890.
This would seem to place her in Bradninch in 1911, as a servant. In 1901 she was in Clyst Hydon with her family:
Edwin John 46
Mary Ann 39
Edith 12
Lucy 10
William 8
Frederick 6
Percy 4 (transcribed by Ancestry as Perry)
Charles 3
Walter 2
and there are two more children:
Helena abt 1902
Dorothy abt 1904
That is a load of siblings of Lucy Webber Veale -- aunts and uncles of Leonard -- whose descendants you could look for. Their children would have been Leonard's first cousins, and it's even possible some might be living today. And some might have children born, say, in the 1930s, who are still living and who remember him.
Someone else could do this, but you could do it easily:
Go to FreeBMD and find the birth records for the children in St Thomas registration district, and get their full names and approximate birthdates (quarter of the year).
Then look for their marriages (remembering for searching that after 1911, only middle initials are used, not middle names). Hopefully, they won't all have married Smith or Brown. Then look for their children's births, by the two parents' surnames.
Here's the easiest one:
Percy Edwin H Webber, birth reg St Thomas, Sep 1896.
... Well, it was supposed to be easy. I don't find a marriage or death.
Fortunately, they seem to have complex and unusual names.
Helena Gladys M Webber, birth reg St Thomas, Dec 1901.
Married Albert H Richards, St Thomas, Jun 1925.
There are 3 Richards-Webber births in St Thomas: 1928, 1931, 1933, and also births in Penzance 1934 and Devon Central 1937, 1940, 1941.
Then it is wise to rule out the possibility of another marriage accounting for some or all of those births. That is the only marriage in St Thomas. There are others in the same timeframe and general vicinity, and in particular one in Penzance in 1933 that would account for that 1934 birth. But Devon Central covers the former St Thomas (including Clyst Hydon), so I would think the births there belong to this marriage.
You also want to look to see whether any of the children died in childhood.
That gives you quite a list of people to look for, just from the marriage of one of Lucy's siblings!
In terms of passive "looking", you can add postems to records at FreeBMD: a short note explaining that you are looking for relations of Leonard who was a friend of your family, and giving your email address so any family member who researches the family there can contact you. (A permanent, anonymous, online email address like at gmail is best for this, and most online uses, so you never have to worry about changing ISPs and not getting messages, and you don't expose your own identifying personal information.)
For active looking, the phone book and google are good places to start.
Unfortunately, Helena's family doesn't offer the best prospects ... Richards is a very common surname. Hopefully, some of Lucy's other siblings produced more easily traceable children.
http://freebmd.rootsweb.com/cgi/search.pl