I did this conversion in late 1993, using a low starter MGA 1500 gearbox. I have since run a stock MGB pressure plate, then a competition pressure plate, then another new stock MGB pressure plate. I have also used both early 1500 and mid 1500 type low starter gearboxes. There has been no problem with clearances in these setups. However, there may be a slight interference issue with the MGA 1600 high starter gearbox, and a more serious issue with more recent MGB replacement clutch covers. When installing the MGB clutch into the MGA, you may run into some of the following issues:

August 2004:

At 05:42 PM 8/5/04 -0700, Steven Devine wrote: >a.) I used the 59 late 1500 gearbox that came with the car [same as the 1600 gearbox]. >b.) There was just enough material up by the high starter hole to interfere with the rotation of the Borg and Beck diaphragm. It would drag just enough to stop the starter from turning the motor over. .... I noticed the scuff marks in the inner portion of the bellhousing right next to where the hole for the starter goes. I took a little material out and fit it back together. Everything was free wheeling.

May 2005:

At 06:09 PM 5/13/05 -0600, Stan Watkins wrote: >The Hazel Quinton pressure plate had a tremendous amount of interference with the side of the transmission (1600 high mount starter). I'm not sure one can remove enough material from either the transmission or pressure plate to make it work. The Borg and Beck pressure plate is somewhat flatter and only had moderate interference. I ground a little material off the transmission and it fits fine.

October 2010:
Now we have a report of similar MGB clutch interference with the bellhousing of the Ford T9 5-speed gearbox conversion kit for MGA/MGB supplied by Hi-Gear Engineering in the UK. These kits have been available for some years without such comment, so this may be an issue with a recent change of design of the clutch cover(s). The issue has been reported to Hi-Gear.

Current report shows the Borg & Beck clutch cover interfering between between 9 and 12 o-clock position inside the bellhousing of the 5-speed kit (above the starter location).

On 7/21/2015, Dominic Clancy in Zurich wrote:
"The report of interference of the MGB clutch covers with the HiGear kit was from me. It was eventually traced to a new casting method that Peter Gamble had not been told of. The castings were sagging slightly as they cooled. He told me he modified the design slightly to take account of this and prevent future problems".

From prior reports pertaining to the standard MGA gearboxes, the Quinton Hazel clutch cover may have more interference than the Borg & Beck unit. Photos below show the difference in shape of these two parts.

Old Borg & Beck clutch with tapered sides.

New Borg & Beck clutch above is similar to the Quinton Hazel clutch below.

Red marks indicate where parts may interfere. Rotate engine by hand after assembly with gearbox to verify clearance (or interference) before trying to crank start engine. Immediate fix is to grind some material from inside of bellhousing at point of interference. Do NOT try to modify the rotating clutch cover, as it would disturb the balance, then needing to be re-balanced after modification. This would also require modification of a replacement clutch cover in the future.

For some time the Borg & Beck clutch parts have been packaged in AP boxes. AP Driveline already owned Borg & Beck. Magal Engineering bought out AP Driveline when that company went bankrupt in 2009. AP driveline is a now Division of Magal and uses the Borg & Beck name.
This is a picture of the new Borg & Beck MGB clutch inside the MGA 1600 bellhousing with some grinding of the interior for clearance.