Using your UK destination as your address, you could get insurance from a UK company over the phone. I was offered 365 day overseas use on my camper van by Adrian Flux Ins. But any period that gets you from ‘abroad’ to UK will do.
Once insured for ex-UK travel, book an MoT in UK for the day of your arrival. This does not have to be at your port of arrival. I checked with DVLA and was told that as long as it was a confirmed booking it could be anywhere. On that basis I drove from Valencia - Calais - Dover to Minehead, in Somerset, for the test because if there had been any issues, I would be only 5 miles from home rather than +/- 200.
If you want an MoT as soon as you get off the ferry, there is an excellent MoT garage in Dover, <10mins from the docks. I have had two vehicle tested there. They bent over backwards to get the necc repair done in time to leave the same day.
Wherever your MoT is booked get them to send confirmation on an email with their company details on it, so you can print this out. You have to be clear to make them understand why this is important. This should pacify any passing Plod who wants to see your papers.