I have exported my car from the UK to France. I am in the process of registering in France. I have the CT and French insurance but as yet am awaiting the carte Gris with the new French registration number etc. So I am still driving with a UK registration. I need to drive back to the UK shortly and worried that I will not be covered in the UK. I still have a valid UK tax and insurance but no MOT. Can anybody advise what I am covered for in the UK?
If the car is still registered, taxed and even insured in the U.K. as you indicate, who is going to ask questions? But set up an M.O.T. as soon as possible, and try to carry evidence of the booking. A waste of £40 or so. And with luck you will get the French Carte Grise in time: they are normally quite quick. I assume you will travel on a U.K. passport. The golden rule is to stay inconspicuous and never ask questions.
ANPR cameras at the UK ports and in Police Cars will flag the car up as no MOT very quickly and there will be other problems if you have SORNed it in the UK. The UK authorities have wide powers to seize unlicenced vehicles to remove them from the highway. The lack of an MOT is a criminal offence but this can be circumvented by arranging an MOT close to the point of entry to the UK.
I would think that you might stand a better chance of proving intent if you have notified the DVLA in the UK of permanent export and can show documents (an online receipt for example) that you have indeed applied to register the car in France and if old enough, you have a French Contrôl Technique which is valid in the UK.
IIRC there are long delays in the issue of Vehicle registration documents (Certiciat de Immatriculation) in France following the introduction of a new on-line system which you might (I say might) be able to short circuit by asking a local Garagiste to do it for you. It will require the CoC which, in the case of a relatively new vehicle will form part of the UK registration document.