We had a similar thing in our kitchen last year.

The central heating hot water tank burst and brought the kitchen ceiling down.

The insurance wouldnt pay for the replacement of the tank, but did cover the damage caused by the burst.

Whole new kitchen ceiling and dining room ceiling, re plaster 2 walls and decorate throughout.

Took a while with ours cos they "alledgedly" found less than 0.5% asbestos in the old artex covering on the plasterboard.

The insurance process itself was easy enough. Just make sure you claim for absolutley every single thing thats damaged.