Thank you very much for your replies. They are very helpful and the location is also very interesting.
My ancestor Wm Richardson is on the Birkenhead Census in June 1841. His address is 'Price St' but under him are two entries for 'Brunswick Terrace'. Above him is a family living at 'The Meadow'.
When his daughter is born in October 1841 his address is Brunswick Terrace, Price Street. I think that is most likely the same place as in the 1841 Census.
What is interesting too is that on the 1841 Census his occupation was listed as 'School Master'. Wonder if he taught at the Brunswick Quacker School.
In his obituary in the Gentlemans Magazine in 1851 He was a Reverend but it says he recently kept a private School at Birkenhead. He died at Claughton.
In1857 this is the marriage of another daughter:-
Chester Chronicle, Saturday, 12 Sep 1857, page 5
2nd inst., at St. Saviour's church, Oxton, Cheshire, by the Rev. W. Cocknoft, George, second son of the late Rev. George Burton, of Lincoln, to Maria Eliza, eldest daughter of the late Rev. William Richardson, of Hamilton-square, Birkenhead.
It seems he was of Hamilton Square - that is very close to Brunswick Terrace.
The question now is are there any records of a Private School which he could have kept around that area of Birkenhead in the 1840's.
Judy