Distributors between the A Series and A+ engines are not interchangeable.
The A Series Engine uses a 45D or 25D Distributor
The A+ Engine uses a 59D or 65D Distributor
Mini A Series Distributors (up to 1980) are held in place by a pinch clamp and 2 bolts.

Mini A + Distributors are held in place by a Y clamp and a single bolt.

To identify the difference between these two engines, read on…!
Much has been written about the A Series engine, and one of the best articles is this one written by AROnline founder Keith Adams. It’s a great place to read more detail about the ins and outs of the A Series engine and it’s history and development.
The A+ engine came on to the mini scene in 1983. It has a thicker block to box flange and is generally more robust than the standard A series. Operationally it’s pretty much identical and is the same capacity. Heads/boxes are swappable.
Here are the A+ distinguishing features:
• Strengthening ribs on the back of the block at the clutch end
• Thicker block-gearbox flange
• Dizzy clamp is a forked plate with a single bolt into the block
• Dipstick sits directly in block, not in a tube, and is shorter
• Verto clutch, slave on plate slanting downwards, short arm. (NOTE: The very first A+ engines had a pre-verto clutch)
• Alternator bracket mounting holes are closer to the rad on the A block
• ‘A+’ stickers on rocker cover if a Metro!
NOTE: The 1275 crank fouls the inside of the gearbox casting on earlier 1960s unless the ‘box came off an “S” originally.
They standardised in ’68 or ’69. The changeover to A+ didn’t occur on all parts at once. Some engines had eg: A+ block and pre-verto clutch, and some had A block/box and A+ bits bolted on. Maybe BL running down stock.
One correspondent has an A+ engine as described above, but it was the original engine from a 1981 New Zealand model 1275GT. It does not have a verto clutch, but the gearbox is the A+ type, and so is the block. It could have just been a test by Austin-Rover to see if their engine was any good before it was released in the UK in 1983.
It is possible to put an A series engine onto an A+ gearbox and vice versa, but the transfer housing and drop gears *MUST* be the same type as the gearbox, as the idler bearings are different sizes. Apart from that nothing to it.
Home brew Engine Decoder shows weather you have A series or A+
A Series and A+ Distributor Drive differences: