Turns out this is not the old TJ Davidson Rehearsal studios. The original one was torn down in the 1980's --- then a car park was built over it. Got this info during my visit to Manchester. A musician very close to Joy Division members confirmed this info. What you have posted is another famous landmark associated with Oasis.
I've seen Grant Gee doc many times. The building does resemble what you posted --- and I walked by this building last weekend as well. It does look very close. But, any of the older buildings in that area will resemble the original TJD's. Here's one of the blogs posted by a local Mancunian, indicating that Little Peter Street WAS once home of TJD's. And, describes the building you captured as The Boardwalk (associated with Oasis, as my other Manchester source indicated). I am convinced that in this case our 'map of the stars' got it wrong.
Also, look at this listing for a Flat for Sale. If you scroll thru the pix, you will see that inside the flat, you could claim that LWTUA was shot there long ago. But, fact is all the buildings there looked like that both inside and out. www.rightmove.co.uk/property-for-sale/property-23795577.html
That's the area, but my understanding is the actual building was torn down long ago. As proof, you won't find a building that matches the number and type of windows in the famous Joy Division photos that were taken there in 79/80.