I'm running Cooper S discs (no booster) with 5/8th rear cylinders and under quick/heavy braking while cornering the back gets a little loose/wobbly. it's easily controllable I've just noticed it a few times.
Is this a normal thing?

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Respect mine and I'll respect yours.

Yes under heavy braking with good front discs, LOTS of weight gets transferred from rear to front. Moral... don't do emergency braking in corners, unless your reflexes are FAST!
Years ago I had a pic of Peter Manton? braking for creek corner at Warwick Farm, with both rear wheels off the ground...

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DrMini- 1970 wasaMatic 1360, Mk1S crank, 86.6HP (ATW) =~125 @ crank, 45 Dellorto (38 chokes), RE282 sprint cam, 1.5 rockers, 11.0:1 C/R.

I have had a few nervous moments while braking into a corner. But that was in NAV with drum brakes and very little fuel left so the rear was lighter than normal.
The hardest thing I found to do was get off the brakes and get onto the accellerator when going sideways to pull out of it.

Lift off oversteer is scary fun too

I miss driving NAV, must get round to fixing him one day.

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Do you have the same tyres on all four wheels plenty of tread

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"Show me the Mini!"

Had you just eaten a curry or had my mothers cooking?

no...

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did I tell you that I won a trophy?

Silly question are both rears adjusted equally? when they are out of adjustment Lillee tends to not break straight. When they are all's good

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Lillee - 1969 Morris Mini K

Break or brake?

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Dab the brake, flick the wheel and keep it pin'd

Brings back fun memories and some of soiled undies

well why the hell are we braking heavily in corners?
slow in fast out.
or am i missing something?

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the mokeman cometh...........

It's normally when people pull out in-front of me on roundabouts
I guess I just have to be ready for it in the future.

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Respect mine and I'll respect yours.

pay attention to 9YaTah's post.
what tyres are you running, how old, and what sort of condition?
It could be an important factor.
KB

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Brand newish Falkens on all four corners, that's not an isue this time.

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Respect mine and I'll respect yours.

Back end getting loose

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Stop Licking the Dog...I Don't Care Who Started It

Minis transfer weight easily under braking, they will get light in the bum just from backing off. You need to be aware of this at all times as they will spin quite easily if you do the wrong thing. (though no where near as bad as an early 911 Porsche)
You can brake in a corner but you will need to steer the car to keep it pointing straight.

People that say "don't brake in corners" just don't live in the real world! I can think of a lot of places where you just have to brake in corners. It is not as if you can run a red light with the excuse "I can't brake in a corner" You have to be able to stop the car at any time.

My advise is to find somewhere open and safe and practice braking and backing off in corners. But find somewhere safe to do it.