The Building Regs themselves are very general. In effect, they say the structure must be strong enough. The Approved Documents (ADs) have a lot of detail; if you comply with the approved docs, that is automatically “deemed to satisfy” the Regs. If you don’t meet the ADs, and you can prove to the Local Authority that the floor is adequate, you would still meet the Regs – the difficulty is convincing the Authority. If you get a structural engineer to do actual load and deflection calculations for the maximum load you could reasonably put on the floor, that should work.
But, as above, you only need to meet the Regs at new build or major refurbishment – the insurance company are probably regarding the work as refurbishment to reduce their risk. But if refurbishment is a consequence of the insured damage, they should pay!
If you do decide to strengthen / stiffen the floor, rather than use steel, I’d put extra joists in, centrally between the present ones. Something else that would help (a post above mentioned solid blocking) is to fit short sections of joist sized wood between the joists, near the ends, at right angles, to stop them twisting on the joist hangers. If the joists can’t twist, either by being blocked or built in, their nominal load capacity would be higher.