The line through Leigh station
was actually proposed for closure in the 1963
Beeching Report Part 1.
The service is listed in Appendix 2, page 104 as "Liverpool Lime St - Tyldesley - Patricroft - Manchester Exchange (Local)", under the
Passenger Service, Line and Station Closures section.
By this time, many of the stopping trains on the ex-LNWR Liverpool/Manchester route were diverted at Kenyon Jn onto a loop through Leigh and Tyldesley, rather than travelling directly across Chat Moss. They rejoined the main line at Eccles (and never served Patricroft station - Beeching obviously got confused!), meaning during the 1960s Leigh had direct trains to both Manchester Exchange and Liverpool Lime Street.
This line actually hung on for a good few years until May 1969, unlike many of Beeching's targets, the majority of which closed in the mid-1960s (including the Manchester - Tyldesley - Wigan NW local trains).
I don't think closure of the "Leigh Loop" had anything to do with withdrawal of PTE funding. SELNEC PTE only came into existence on 1 April 1969, literally weeks before Leigh (and Tyldesley, Worsley & Monton Green) stations closed. British Railways would have had their closure plans well in hand before the PTE came along, and it took until 1972 before SELNEC PTE took over responsibility for funding local rail in the Manchester area. It was the final stage in a rolling scheme of closures in this part of South Lancashire, and BR had ripped up tracks and dismantled bridges on the Leigh line by October 1969, so there was no chance of any reprieve!
One explanation I have seen for BR wanting to be rid of the line was extensive mining subsidence throughout the area, requiring frequent and ongoing repairs at a cost totally out of proportion to the traffic on offer.
The two books "A Lancashire Triangle" (Parts 1 & 2) by Dennis Sweeney give a lot of interesting history and some excellent pictures of former railways in the Leigh area, if you can access them at a library or direct from Triangle Publishing (I don't think they're available from Amazon and the like).