Not that I've done much research into bitconnect or had any dealings with them (since I heard so many negatives) how could they realistically shut it down? Unless the site is hosted within the UK they simply move servers elsewhere. Getting a block put on the UK ISP providers for that site will result in multiple mirrors setup or simple VPN to bypass.

That's the good and the bad blockchain technology, you cant shut it down. But ultimately it means scam companies can continue to run their business unless the community decides to kill it off.