I do not expect that it is possible to rent a car in the UK without the legally required insurance (not through any reputable hire company anyway).
However, I have noticed a difference between here and the US which might explain your confusion. I believe that a typical US personal car insurance policy covers you when renting a car so it is sensible for even legal cover to be optional when renting. I used to work for a US company and we were instructed to decline all insurance when renting as it was covered by the company policy. Here in the UK, this is not normal. My personal policy will cover me to drive a friend's car but not a rental. Hence even local customers need the legal insurance. So, it is not usually optional as everyone needs it.
There is also Moo's point that legal required cover is only third party. So, for my own car, I can choose whether or not to have comprehensive cover so that damage to my own car is covered. It will be a business decision of the rental company whether to force further insurance on to you or trust that you are covered in another way. The law might not require them to do so but it also does not require them to rent a car to you at all.
While typing that, I saw your continued discussion with Moo. His further comments are convincing. If you damage the car, they will need to claim against you and they would need to trust that you could and would pay them.
Again, there seems to be a UK / US culture difference here. In one of my of my early visits to the US, I was surprised to find that insurance was optional. I asked what would happen if I declined it and the car was stolen. I was told that they would bill my credit card for the cost of the car. I decided to accept the insurance. I would not expect that conversation here.
Some extra detail and clarification. This my experience:
Legally required cover e.g. third party - no option.
Some level of insurance for the car itself - no option. By some level, I mean that you may be liable up to a limit if you don't choose CDW. I have not seen optional theft cover or optional no damage cover at all.
There may be an optional CDW which removes the limited liability that I just mentioned.
I find this very different from the US where you can rent a car with no cover at all, not even legally required cover.
If your employer has a special contract with the rental company then it could be different. I used to have an employer with such a deal. When I rented a car via the company account, I got a special low price because it did not include insurance. I was covered by the company policy. I don't think that this is an option for an individual that rented car.