roll up the wet carpets and put outside so the insurance assessor can view them (assuming you have new for old cover, they will pay for supply and fit of new carpet of equivalent quality, or other flooring at the same price. You are not obliged to go to their preferred supplier but they may knock a bit off the amount if not as they get some kind of kickback commission. If the insurance co's damp contractor takes the carpets up, make sure you keep a small sample from each room for the assessor to view later.
When it happened to me they wanted me to go to Carpetwrong with vouchers, but I got better quality for the amount from a local independent trade supplier (who also fits carpets in commercial and domestic customers). I was able to buy more of the same for undamaged rooms, paying privately for supply and fit at the same time, and as he priced it as part of a large order, the balance I paid was very reasonable.
You need the floor to dry out, if it is a wooden floor, it can dry from air through the airbricks, but will be quicker if you take up a few floorboards. A concrete floor needs to be exposed by taking up the floor covering.
In my case the insurance co appointed a contract manager company called Chemdry, I had a substantial claim and the service and builder's workmanship was very poor, I now wish I had engaged a loss adjuster or similar to work on my behalf, even if I had to pay him out of my own pocket.
If you need beds and bedding in a hurry, speak to the insurers, it should be OK if you have the receipts and the quality is the same, but say you want an emergency interim payment for it.
Any modern furniture or kitchen cabinets is likely to be made of coated chipboard or MDF and will be ruined by damp.
Take the electricity meter readings at start and finish of dehumidifying because the machines use a lot and you can claim for the cost. They do however provide some warmth so your gas bill may be a bit lower.