This estate is even harder to track down than the Heaton Park one was!
The Manchester Guardian digital archive (pay to view or through a Manchester library card) had 6 hits on a search for Blackley Prefabs or Prefabricated Boggart (!), but the only photos I have found so far are of the demolished sites at Blackley and Heaton Park. They are alongside a Guardian article dated 4 Jan 1967 (discussing the future of the sites, and whether they should be returned to parkland or have permanent houses built on them). It describes the Heaton Park and Blackley estates as 'recently demolished' so if that is correct, they had come down before 1967.
An earlier article dated 15 May 1964 suggests that the prefabs had been cleared, or were being cleared in that year:
"The Parks Committee [of Manchester Corporation] has prepared plans for a sports centre on the site at Heaton Park, where prefabricated houses, built just after the war, were demolished recently, and a nine-hole golf course at Boggart Hole Clough on the former temporary housing site.."
so your grandmother probably left just before the demolition programme started.
Another article dated 1953 states that they were only intended to have a 10-year lifespan and that "..in Manchester alone, a thousand permanent homes would have to be found for the prefab-dwellers in 1955-56, when the 10 years end..."
meaning they were constructed between 1945-6. This seems to fit with people's recollections on the rootschat Heaton Park threads.
http://www.rootschat.com/forum/index.php/topic,278711.0.htmlI did find out that the Heaton Park prefabs were built by the Manchester architects Fairhursts, so possibly that firm had the contract for all Manchester's prefab estates.
Hope someone can turn up a photo for you

Barbara