If you go to www.screwfix.com (or a competitor who is currently trading)
and
search for "tap reviver" you will get what you need - replacement innards.
You can usually re-use the old handles if you want them to match.

Alternatively, you could just replace the entire lot with a proper ceramic
cartridge tap. I have never fixed a tap washer in my life (unless you count
replacing gland packing on outside taps and stopcocks).

The reason that washer type taps seize up is to provide a reminder that you
haven't replaced it with a decent ceramic tap yet.

Christian.