Brake juddering, failure: ABS or master cylinder, or anything els

Car occasionally suffers form brake juddering/failure (during a sudden brake: the brake pedal can sometimes, mid-pump, vibrate and lose all power and tension- sort of dropping to the floor)- requiring immeidate second pump in order to brake porperly.

Discs, pads are new. Calipers are ok. Fluid is new.

I have been told it could be the brake master cylinder, but this problem happens at the start of a journey just as frequently as at the end of a long journey- so perhaps no overheating problem. Or could there be something else?

Perhaps the more likely problem is the ABS. I haven't noticed the light go on ever, but it is exactly obsucred from my sight whilst driving by the steering wheel (annoyingly). And, when the brakes fail, for that split second I'm more concerned about not crashing into a car head-on than looking at the dashboard. So might have missed it. When the car starts up, all is fine- the ABS light pops on and then off.

What could the problem be, how should I get it diagnosed (is this even possible, or is it just guess work) and how much might it cost to fix.

I suppose my main concern, is a precise diagnosis. Can this be done. A mechanic did tell me, that it is very diffiicult to know until the whole system fails (scaremongering?!). And he said it would be very expensive.

But if it was just a dirty sensor, is there any way of telling this? Or do I just have to wait until it does/doesn't happen again.

Also. The car failed an MOT 5 months ago for brake juddering. £200 solution- new discs and pads = no solution at all.

Thanks