What’s impossible about it? It’s the exact position I found myself in- most insurers wouldn’t insure without an MOT. Solved it by just saying **** it and driving to the test uninsured.
You said insurers would ask for a certificate of insurance, not MOT.
I’ve never been asked for a MOT and at no point has anyone everasked me to prove my MOT status when taking out insurance on SORN’d cars to take them for their MOT (I do it twice annually),FWIW. I think they have clauses in there saying they’ll invalidate your insurance if your car is not roadworthy, but that’s legallydifferent from not having an MOT.
So long as its insured you can drive to the MOT stationto get the MOT, then to the tax office to get the tax for it on the way home…
I take mine to a local garage who are usually very fair and know I’ll usually replace rather than repair and do my best to get it ship shape before taking it for the test (they hate being used as the annual service test). They seem keen on replacing light bulbs I know are perfectly OK when it goes into the test place, which can be frustrating.