Thanks for the explanation. I was very new to DNA testing and hoped Living DNA would offer a Williams. There were a few Welsh sounding surnames, and many more English sounding ones. There is one Thomas Williams, born 1836 that fits the location. He was illegitimate, but names John Williams as the father, then baptised under both surnames. I was hoping, he would have fathered other children, and any males would also have the same Y-DNA.
Thomas Williams only appears in two reliable census records. His age is always two-years younger than his wife, but neither were fully accurate. I traced her and she was born in 1834. That makes me think 1836 is correct. Finding another Williams may be difficult. His son Thomas had two sons and three daughters who actually married, but only one of those sons had children. That was another Thomas who had one son and four daughters. Basically, there is me and possibly a male cousin who I have not met in 60 years. He too would have the same Williams Y-DNA. Hoping Living DNA would offer a Williams, I now realise it was a long shot.
If there are any Williams, with the same Y-DNA, apart from my cousin, it would have to be from John Williams. I will now look into 23&Me.