On the face of it, £7k sounds a lot, but if you break it down..........
Over £1,000 would be VAT.
Depending on access, it may be up to £1,000 for the scaffolding.
I've no idea of the size of the roof, but there is the cost of the new tiles/slates. If slates, then that would cost more than concrete tiles.
There could be another £1,000 for leadwork around chimneys/rooflights.
Although a quote should never be loaded for the sake of it, no one is going to re-cover a roof on three storeys for a cheap, budget amount. The cost of having to go back over any later problems would be substantial.
I'll be interested to see other quotes, Wolfers.