In your case you will have 2 policies, the Gov one, which is COMPULSORY, and your private cover......
I think the reason for the gov one is that a huge number of the populace would not have any insurance, so third parties are not covered for any injuries caused by another.
So folk must pay it to get the road tax sticker, which is a step in the right direction for the BiB looking at a windscreen.
My own opinion is that if you have private insurance, which is way better than the gov one, you should not need to have the gov one...