Probably too late now, but we did not use the Local Water Authority to lay the service pipe or any pipe on the property. We used a Local WIRS contractor. Much cheaper, and easier to deal with, as very small company.
https://www.lrqa.com/en-gb/utilities/wirs-wirsae/
You mention Openreach are a nightmare, but there would be no problem negotiating with the new owners and running a cable from the old house [as suggested for the electric] , also Your contract will not be with Openreach it will be with a provider, who should give you compensation for being late. We managed to get £180 compensation, but we had to ask, as the were so late - It was in my advantage not to chase them though.
We didn't move into a caravan, but I am not sure if it was on this forum or another, where someone, got a shed, and made it as a walkthrough at the door of the caravan, so they could leave mucky boots, and clothes and get changed to, so the muck did not encroach into the caravan.
As others have said, it's time to think of yourselves,