Okay, for a start if you go to
http://www.1911census.co.uk/ you can find the family in 1911; there seem to be these children other than Violet (also their mother, Rose), including a Patrick:
http://freebmd.rootsweb.com/ is a good place to look for their births, marriages, and children. I won't list the possibles (one more post I think and you can use private message) as quite a few of their children are probably still alive, but for an example:
Patrick's birth is listed as "Patrick James A. Carroll" and his marriage as "Patrick J. A. Carroll" (in 1923), to Martha Bridgland.
If you search for births, and put surname Carroll and mother's maiden name Bridgland, you will see the births of their children (including Georgina and Francis).
If you are hoping to make contact with relatives you might try writing to local newspapers.