If you mean the caliper, then stop driving the mini and talk to MiniSport .... this is very serious
All things flex (semi solids and solids anyway) but if you can actually see it then its very wrong in this case !
Dont want to jump in here sounding like I no it all but a few years ago i had a vtec conversion and at the same time had a big brake conversion all brand new.
It was a hole kit from AP and fitted by a mini specialist it had all the fancy hoses and everything was new even the rears which were standard mini. Anyway to get a solid pedal you had to double pump, we checked everything but everything was good, the garage said it was the calliper flexing which you could clearly see, so Monday morning the garage called Ap up and explained what was happening and they said it was normal to see a calliper flex as it was doing, the pressure applied at this point should be enough to stop the car .
In the end It turned out that the master cylinder which was a new metro turbo one counldnt supply enough fluid in one pump to the callipers. When they fitted a servo to it the brakes worked and felt right.