I had a couple of P3000s in that size fitted to my car and didn't notice any difference from the Michelins I had up till then, so I would doubt that the tyre make/model is the problem. Those are the smallest tyres that can be fitted to the Mini and that helps keep the noise down.
It's more likely that it's the Mini that is the noisy part, not the tyres. My convertible has a lot of tyre noise, but I don't think the hatchback is hugely quieter.
Obvious things are: have you got the rear seat up and is the parcel shelf in place? Those both reduce noise from the rear of the cabin - and I think it's from the rear that tyre noise is most noticeable.
But fundamentally I think you've changed from a quiet car to a noisy one.