If I park a trailer on the street, and then park a car on top of the trailer, do I need a permit?

I am looking for cheap ways around car insurance / parking having moved to London.

I don't want to re-register my car's address in London because the insurance goes up nearly £800, but I can't get a residents permit without doing so. I have a trailer at home in the country on which I can park / transport a car - what happens if I park that on the road, get a permit for that, and then park my car on top of the trailer? Is my car technically part of the trailer and is the trailer's permit therefore valid. I feel like I would need to register the trailer for a parking permit of some sort still, but this would still save me £800 on my insurance.

Weird question, I know, but I can't be the first person to think of this! I also know it probably wouldnt work, but no harm in asking.

Thanks