The only Ukrainian Greek-Catholic Church I'm aware of in Wolverhampton is that served by Father Matyczak - and it is indeed a nice church. I was there once with Bishop Paul (Vasylyk) who was visiting Ukraine (he had come to England for a conference at Ampleforth about the Christians in the fast-collapsing USSR).
Incidentally, the Cathedral in Mayfair had been a Congregationalist church known as the King's Weigh House, not a Methodist church. The last Protestant pastor was Dr. Orchard, who himself became a Catholic and led most of his faithful into the Catholic Church.
Fr. Serge