No car goes forever Maybee70 and at 17 years old, it’s more than possible for a car to fail its MOT from one year to the next. That sounds patronizing - I don’t mean it to be. Try googling the importance of shock absorbers and what they do, as I’ve just done, but it was interesting to see an approx cost of up to £500 given. I don’t know if that’s per absorber, so if all 4 of yours are going, £2K is about right. Is it worth getting a price from another garage, as yours seems a little hasty in pushing for the work, especially as the car has passed its MOT.
What I’d think about, is that the repair is going to cost as much as the car is worth and as Merlot says what else might go, especially on an old car.
Obviously, I’ve no idea of your circumstances, your age and how much longer you hope to drive, but personally … I’d start looking for something else, while you’ve a long MOT and trade your ‘banger’ in. I’ve had an old car in the past, but a classic car and threw money at it, but in the end my head had to rule my heart and it had to go.