We’re becoming very confused here!
“if a car is not Taxed nor MoT'd - can it be insured”
As has been explained, Since you cannot tax a car without a valid MoT certificate, nor drive it to an MoT testing station unless it is insured, then insuring a car without either is not only permitted but is essential.
“I believe it can be insured, but in the Sade of a claim, you wouldn't be covered, so there'd really be no point”
That is incorrect. The cover required under the Road Traffic Act (Third party injury and damage) cannot be invalidated for a lack of Tax or MoT. Cover against accidental damage to the insured vehicle MAY be restricted in the case of no MoT but the insurer would have to show that the lack of MoT contributed to the damage caused. There are no circumstances that I can think of where lack of tax could invalidate cover. In fact I seem to recall a case a few years ago when an insurer tried just that. He had a clause in his policy Ts & Cs which invalidated claims for untaxed cars. It was rejected in court and I believe no insurers now have such a clause.
You can check whether a car has valid tax and MoT here:
https://www.gov.uk/check-vehicle-tax
And you can check if a car is insured here (you should only use it for your own vehicles):
http://www.askmid.co.uk/
The Motor Insurers’ Bureau runs a compensation scheme for the victims of uninsured drivers. The scheme is funded by a levy on all insurers (essentially, those who pay for insurance meet the costs of claims against those who don’t):
https://www.mib.org.uk/making-a-claim/what-we-do/
The situation with vehicles is quite straightforward. All vehicles must be either taxed or SORN’d. If they are SORN’d they must be kept off public roads at all times and not taken onto them until the SORN is lifted. If they are on the road they cannot be SORN’s and they must be continuously insured and taxed (not just for the period they are driven). If they are to be driven they must have a valid MoT certificate.
The sequence of events to get a SORN'd car back on the road is:
1. Lift the SORN
2. Get it insured
3. Get it MoT'd (only by driving to a pre-booked test)
4. Get it taxed