One reason, among many for the decline is that 'back in the day' it was often done after a birth - relatively easy as the uterus is 'high' and the Fallopian tubes more accessible.
When NHS funding models changed, maternity units were not paid for the extra night or two that a woman might stay in following sterilisation.
Also, vasectomy is, on the whole, a cheaper & simpler option.
VioletSky, I completely appreciate what you are saying, but this can be difficult. As a student nurse I was assigned to a gynae ward with a very well respected consultant who specialised in reversing sterilisations (in fairness, these days, you would do IVF instead). In the space of 3 months I nursed:
2 women who had threatened suicide if refused sterilisation in their early 20s, and had changed their minds.
2 women who had all their children die. In case of recognition here, I won't put the circumstances, but they were very distressing.
Personally, when discussing with my consultant, I said that I felt that whatever happened, I was 'done'. I also think that we should consider, and take responsibility for our decisions; but I do understand why some doctors feel reluctant.