Burke's is a bible to me. There is Burke's Peerage and Baronetage and, in this case, Burke's Landed Gentry - the one I have copied from is the 1952 edition and the entry is for WINSTANLEY dormerly OF CUERDEN HALL, although there is also an entry for WINSTANLEY OF BRAUNSTON.
I cannot see any connections to London apart from Alice Nellie Winstanley, daughter of James W of Freshfield, Maghull nr. Liverpool (she married 24/6/1901 Benjamin Pratt of London and had one son and one daughter). There are some connections to Ireland and one Winstanley who emigrated to Australia.
Most of the works I have consulted have been centred on Lancashire because that is where the Robert I am searching for came from.