Definitely do not mention the names of any living people on here as stated in previous posts. As for more generic advice you will need to look for the marriage of the couple and then search for any children born with the mother's maiden name around a logical time frame. You do not need to know their Christian name but this method should tell you. This relies on the parents being married. This can be done after Sep 1912 (from memory) on FREE BMD:
https://www.freebmd.org.uk/I think this cuts off around 1987.
Find my Past (a UK-based subscription service) is also excellent for this.
The GRO register also offers "Search the GRO index online". This serves the same purpose.
I would then look on the UK Electoral Roll on FindMyPast or Ancestry. Ancestry often gives you a time frame for the person's birth eg. Mary Smith (1960-1962) which will help determine if you have the correct person. There are also UK-based people directories online, but the name escapes me at present.
I have had a domestic crisis here this morning so I now must go and do a major clean up. I was just filling in time until it was fixed, but I hope this has been of help.