It's not because of the BBC reports directly.
It's mainly the UK government watchdog Ofcom, who have been saying they think this site should be banned in the UK or shutdown altogether, and threatening to take legal action against this site for violating the new Online Safety Act, which has just come into effect, which is meant to protect minors from coming across harmful content online in all forms.
(This is why adult porn sites now have to do age verfication checks in the UK, such as providing s credit card or photo ID, resulting in the massive uptake in the use of VPNs in the last few weeks).
This site voluntarily closed access to UK users, in order to protect it and its users from this hassle.
As their statement says, the UK government has no international authority or jurisdiction (this site is US based), but they chose to anyway.
As well as the various BBC stories, Channel 4 (UK) aired a 2 part documentary on Kenneth Law earlier this year, "Poisoned: Killer in the post", which focused on his activities on and off this site, and this site in general. There are posts to it on here. Worth a watch imo.
But, as is being routinely reported in the mainstream media in the UK, a simple VPN gets around the situation.
HTH.