Keep in mind that most (all?) 850's had single leading shoes which will lower the braking performance. Unless you have a 1275 or a worked engine, I've found the drums to be more than enough, provided that the maintenance is kept up.

The biggest difference I found when going form well maintained drums to discs is that I don't need to do so much maintenance any more. I used to adjust my drums every few months to keep it pulling straight and keeping a good pedal height, now I just need to flush the fluid and adjust the rear shoes. I haven't noticed any major improvement in performance, but I generally don't brake hard time after time, which is where disc brake performance really shines.

Personally I think drums are a P.I.T.A although, they are all I've ever had. I'm not confident they'd stop me very effectively on the M1, but I'm all about "granny spec"!!

I've got standard drums all round on my 998 they are still more effective than my 80 series land cruiser cant afford disks or I would just from a maintenance perspective.

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How would the brakes be improved if I fitted a set of finned alloy drums?

They will cool quicker, so less brake fade, but nothing compared to moving to discs. They're also lighter.

Twin LS drums stop pretty well in road use. I found they are better with new drums and shoes from Karcraft than getting drums machined oversize and fitted with local re-bonded shoes.

IMO a main benefit of discs is their self-adjustment.

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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 got some mintex brakes shoes when I was in the UK last and they seemed to work better than standard shoes from Karcraft

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1969 Cooper "S"
1967 Mini Deluxe
1973 Clubman Van (the fleet spare)
1978 ex 1275 LS ("Wizard" Eaton Supercharged)
2015 HSV GenF GTS(occasional drive & tow car)
2019 MINI F55 Cooper S

I saw the mintex shoes on the minispares website and thought that they might be a good option.

I have heard of Kevlar brake shoes which work as good as disc brakes apparently. Although I have never seen them myself or used them. They were mentioned by Chris Ellis of Bundaburg.

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DID I MENTION THAT I AM THE BEST SUPPLIER FOR MINI ELECTRICAL PARTS AND REPAIRS?
"Let us remove your "SHORTS"

If you are considering a set of discs now would be a good time to import, whilst the Oz$ = 55gbp or so.

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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.

If I changed to cooper s discs would I have to change the brake pedal? If so where do I get one from?

No it will work fine with the stock pedal. And master cylinder if it is 0.70" bore. You should change the rear wheel cylinders to 5/8" to prevent lockup during heavy braking.

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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.

Thanks Dr Mini. I was wondering if I needed to change the pedal.