Large subfloor void - ingress of water in heavy rain

I would start by checking your sales details. This should have been mentioned within the sales data at some point or to you directly, even if only verbally. If it is something that you were not aware of then you have a reasonable chance that the seller/surveyor can be held responsible for the costs of any remedial works... A job for you to point at the solicitor you bought the house through. As for the problem, a pump is a reasonable immediate solution, but not a long term one really. You would want to either make a small sump area for the pump to sit in or get one called a 'puddle sucker' that takes the water as shallow as possible. Longer term, and without looking at the problem, I would try to find out where the water is coming from and either divert it or protect the house from it by having the outside waterproofed. You can find various ways to do it and I'd look at tracing the source by preference and sending the water away. The alternative is to dig round the footings and 'tank' the outside. Whether by plastic sheeting or chemical/paint type method would depend on what you find. Filling the void if the water is till going to be in contact with the fabric of the house, so foundations, is only going to hide, not fix the problem. I'd suggest talking to your solicitor and seeing what they say and then get an engineer in to see what they advise. Not being able to see what is going on in person makes a better answer impossible I'm afraid.

You’re simply getting a quick easy solution ie the pump. As long as there is an air space left below joists the void could be filled up ideally above ground level outside paying particular attention to any dpc on wall. It’s a permanent solution but will involve tons of stone / fill being literally carried into house plus floors lifted everywhere for access.

Get a metal deteter and see if there is a man hole under your floor