Have you got as far as saying that you want it for private use, not commercial? I assume this is your intention. Many Classic Insurers are shy of insuring commercial vehicles as they, clearly, can be used commercially. That means they have an expenditure immediately on a claim, to prove that the vehicle was not being used commercially. That would invalidate the insurance. That is an overhead cost. They can quote it out as an inflated price, but for the inconvenience, while getting as many cars as possible through on competitive quotes, such 'Special' cases are not worth dealing with, when the next caller is on the line.
I have no idea if there is a Commercial Classic Insurance but I would doubt it, and it would be expensive. Otherwise it is Commercial Trade Insurance, very expensive.
Also some insurers group vehicles. Bikes do not go on car policies. Commercials not on car policies. The argument is the risk is different. So some drivers policies will fail to include vehicles you might attempt to add from a differing class.
Might be worth calling the machine after the manufacturer, rather than by the generic Tuk Tuk name. You will then get most of the way through a quote before it becomes clear you have a Tuk Tuk. Incidentally a Tuk Tuk is only basically one version of these machines, I think the Thai one, often with a Dihatsu 3 cylinder engine latterly. In reality a Tuk Tuk is only a development of the larger cc Vespa Ape and Lambro - sold in India.
Surprised at Adrian Flux. The do kit cars and all sorts of rubbish. Trouble is there have been so many Hooray Henry's crashing Tuk Tuks, they have a poor reputation. I think we get about one generic machine accident a year in Oxford alone. They are pretty bloody awful things to drive in my opinion. I bought a number in from Thailand, most went into advertising budgets.