A quick update:
I've now put some puzzle mats down. I looked into lots of different materials, but standard EVA mats ended up being the best for my budget. I bought eighteen 1m^2 mats and asked for them to be delivered to my place of work. I figured they would fit into the back of a car. This is what turned up, on a pallet:
Oh dear. Luckily my boss has a van and his son was kind enough to ferry them to my house after work. Here's them all assembled in place:
Next up I need to maybe cover them with a PVC or similar sheet and frame the whole lot (after I got them home I realised that storing them when not in use would not be an option, given the sheer size).
All brilliant fun