MUFORA operated in the 60s, 70s and 80s founded I think by a local astronomer, Peter Warrington (who wrote two UFO books - including 'Science and the UFOs' based on the first article ever published by a UFO researcher in New Scientist in 1983). I joined in 1974 and we had regular phone ins on Piccadilly Radio around then. We also made a BBC 2 TV documentary on our work in 1975.
During that time we worked with Jodrell Bank on cases and even ran a UFO exhibit there and did lectures in the planetarium to raise money for an ITV telethon. Not without some opposition from the university. We had to - in effect - prove that we were not 'nut jobs'.
The group was always small - on purpose not openly advertised and never more than around 15 members, as I recall. It then broadened its scope to investigate more than just UFOs and moved to the Friends Meeting place near Albert Square. Under the new name NARO (Northern Anomalies Research Organsation) (so called I think mostly so that the magazine could be titled 'NARO Minded') it ran on through the 90s. But as the internet came more to the fore the era of local groups like this waned as everyone could find what they liked on the web.
Personally, I moved to Rusholme when I was four as my dad was from the city and commuting 20 miles in the 50s was tough so we needed to live near his work (Henry Wallwork iron foundry on Red Bank).
I lived in the Manchester area for over 40 years and most of my family still do but I moved away in 2002 and so lost touch with what happened to NARO after that. But I am in contact with some of the members and as far as I know they have not been active in that decade.