Which mintex pads? also try a set of green stuff pads.
I don't know what your service/MOT history is but lots use a decelerometer to check breaking as the car is generally too light for a roller brake test. Your car will pass this even if your rear cylinders are seized. The hand brake still works fine and if the shoes are adjusted correctly that will pass as well.
I take it that you have recently acquired the car by your joining date. So, firstly rear cylinders are notorious for seizing, God only knows why but the Morgan has this quirk! New cylinders cost an incredible £86 for two at best and considering they are off of a Ford Transit van circa 1990 Dick terrapin clearly has the franchise for them! However if you are a hands on chap a cylinder repair kit both sides Is the way to go at £12 each.
If they are working correctly and by that I mean you can rock them carefully side to side with finger pressure then it's check the following:
Brake fluid level and condition, Should be changed every two years or at worst properly checked.
Pad wear on the front and disc state (especially grease from suspension contaminating from discs). It is imperative that this area is kept spotlessly clean and when greasing excess is immediately cleaned from the hub area. These do need correctly greasing however but that's another topic.
Rear brake shoe condition, one shoe has twice the thickness of friction material than the other from new!
Bleed brakes and replace fluid if in doubt. Dot 4 is the fluid unless marked differently at the reservoir.
NB≥
If no joy then check piston function in the front calibers.
Adjust rear brakes with the hand brake adjustment screw on the rear suspension hoop backed right off. check the function of the auto adjuster.
The hand brake is often adjusted to tightly say three clicks and this prevents the automatic rear shoe adjusters working fully. Modern cars want a short quadrant throw bet the Mog needs 5-6 clicks. The handbrake will almost use its full range of throw.
You will then have to inspect the function of the brake master cylinder and the vacuum unit. Check the vacuum hose connection first.
