Yes.
But where are you planning to grease the brake calipers?!
There are only 8 grease points on a Mini (well 9 if you have an early gearbox)
Radius arms
Front top arms
Upper & lower ball joints.
Sorry - just fired this off without checking, of course not the brake calipers 
So would this grease be OK for these grease points or should I get some standard lithium grease as well?
It’s a multi purpose grease so yes you can use it elsewhere. However like like any good practise you always flush it through especially if what you are greasing has not been serviced for a while. Flushing through is just pumping grease in until you see it coming out the same colour as you are pumping in.
Also the Aeroshell PDF I posted will give you compatible greases. So for example Grease 7, Grease 28, grease 33 are all compatible but you still flush them through. In Aviation, certain companies prefer one type of grease over another like the three I have just mentioned. This could be down to cost, availability etc. The Aircraft Maintenance Manual will stipulate types of grease to be used in various components etc, the company in question ( might be orange in colour) wants out of the three in the AMM Grease 33 ( green, stinks to hell) but the Aircraft has been serviced elsewhere ( down route for example) and all they had was Grease 7. This is acceptable by the AMM but when the next scheduled serving is due at home base they will use 33 but pump it through until green grease appears.
BUT this is only for compatible greases. If you use something that is completely wrong so for example a low temp grease in a high temp area, flushing through may not be good enough. In this case a strip down may be needed, all of the incorrect grease/lubricant removed, the item in question inspected / disassembled, ( wheel bearing, plain bearing etc) and then reassembled and greased as per AMM.
Sorry a bit long winded but it gives you an appreciation as to why you can use certain types of grease for the component in question but may need to flush things through.