This is St John the Baptist in Clarendon Park Road, Leicester. It is not a cathedral, but it has been described as "one of the best Victorian Churches in the Midlands". It was built in 1884-5 by the Leicestershire architect Joseph Goddard, who was also designed the new church at Tur Langton.
In the 1930s Major Freer gave four acres of his land to the Diocese of Leicester with the intention that it should provide the site for a new cathedral. However the Second World War intervened and the project never got off the ground.I would like to know the source for this story, but it is possible that it was something more than an eccentricity of the Major's.
There was a Leicester diocese in Saxon times, but the one that exists today was carved out of the diocese of Peterborough as 1926.
I have read that there was some debate over where the new diocese's cathedral should be. St Martin's, Leicester, is not the largest or most impressive of cathedrals and some thought St Mary's, Melton Mowbray, should become the cathedral instead.
So it is not impossible that a new building had its supporters too - one to investigate.