Morning Yvonne
Welcome to the Forum
Built into the brake pad is a small carbon contact at the point where the Manufacturer of the pads believes they are close to the end of their service life. When it makes contact with the brake disc it triggers the light, which is a warning to change the pads, while your brakes still work in a short time uneven wear can occur which will cause damage to the disc. New pads are around 12mm thick as yours have been measured at 3mm there isn't much left see the chart. It isn't BMW or a Garage trying to squeeze money out of you
The MOT I would guess shows the brake pad thickness as an "advisory" all that means they were working on the day of the Test? It doesn't mean they are OK or Safe just that they were OK then.
The only things between us and a wall or ditch are Brakes and Tyres for me it is a false economy to ignore the warning, Pads are much cheaper than a new set of Discs and Pads an complete set of Brembo (Top make) pads for your car I would think is around £40 may be a little more plus fitting which should be around 2 hrs max if you can't DIY
Dave