As you would expect, wagolynn, the DVLA waxes lyrical about being able to tax your car abroad, but conveniently ignores the problem of needing an MoT whilst abroad, with a reluctance comparable to someone telling their friend they should use Lifebuoy toilet soap.
Reading a few related websites, it seems that many UK people staying on the EU mainland long term (typically retired motorhome travellers), find it necessary to make a special, expensive mid-term visit back to the UK to get their vehicles MoT'd.
Without actually stating the fact outright, the various DVLA paragraphs on the subject weedle their way around to what, in essence, amounts to an emphatic, "No, you cannot get your vehicle MoT'd in the EU so as to be valid on return to the UK".
There, I've said it for them! Why could not they have done that?