I've measured the diameter of the splined end, old and new and they
are practically identical. I haven't counted the splines yet. Maybe
they're wider on the new valve.

Any trick I could use to get the cap to fit or must I buy new caps?

I already thought of drilling into the splined brass bushing in the
cap for a few millimetres, then forcing the cap on.

The new valve has cured the low flow problem like magic, but I can't
turn the ruddy tap on or off! (Currently using pliers with a cloth
wrapped around the splines.)

I've seen the plastic spline adapters, but they all look far too
chunky.

How about a junior hacksaw blade in each of the spline grooves?

MM