Simon T formulated on Tuesday :
I was therefore wondering if I could improvise a soakaway by removing one of
the slabs, digging a hole underneath and filling with gravel and placing the
slab back on top, to give water somewhere to drain to.

Would that work? Don't really want to be doing tons of digging, or relaying
of slabs.

It depends upon the sub soil. Once in the soak away, it needs to then
have somewhere to go - a clay sub soil would just collect it. You could
just use a submersible pump, in a suitable buried catch tank, if the
water was first filtered to stop the larger items getting in. Just turn
the pump on when needed.