I've seen a thing like that used to mask the symptom for slightly longer but it's not a solution as such, usually found in minis owned and/or maintained by people who are new to the cars so don't necessarily notice when bits that should be on there are missing.
The point is that there should be no relative movement between the manifold flange and the bell end of the downpipe, so if it's jacked up, the clamp - mentioned by Mr Rusty and myself - is present and correctly fitted and the assembly paste isn't used heavily to mask any cracks or pits that ideally need to be dealt with, then that interface ought to last the life of the pipe.
Here are images showing the shape of the manifold and of the pipe, along with the original clamp. These are standard parts with a three into one manifold and single pipe attaching to it:
miniMETROs, Coopers and 1275s used a three into two alternative so lots of original, smaller capacity minis now have those retro-fitted:
