"We are working round the clock to progress this and get answers into what went wrong and what's being done to fix it," they said.
Technology Secretary Liz Kendall also welcomed the move but said she would "expect the facts to be fully and robustly established by Ofcom's ongoing investigation".
X's change was announced hours after California's top prosecutor said the state was probing the spread of sexualised AI deepfakes, including of children, generated by the AI model.
"We now geoblock the ability of all users to generate images of real people in bikinis, underwear, and similar attire via the Grok account and in Grok in X in those jurisdictions where it's illegal," X said in its statement..
It also reiterated that only paid users will be able to edit images using Grok on its platform.
This will add an extra layer of protection by helping to ensure that those who try and abuse Grok to violate the law or X's policies are held accountable, according to the statement.
With NSFW (not safe for work) settings enabled, Grok is supposed to allow "upper body nudity of imaginary adult humans (not real ones)" consistent with what can be seen in R-rated films, Musk wrote online on Wednesday.
"That is the de facto standard in America. This will vary in other regions according to the laws on a country by country basis," said the tech multi-billionaire.
Musk had earlier defended X, posting that critics "just want to suppress free speech" along with two AI-generated images of UK Prime Minister Sir Keir Starmer in a bikini.
It is unclear how his platform will implement location-based blocks on Grok's ability to edit images of real people to create sexualised imagery, and whether users would be able to get around them.
People seeking to circumvent similar geoblocks on features or content often look to tools such as virtual private networks (VPNs), which can disguise their location online to allow them to use the internet as if they are in a different country.
VPN app downloads spiked in the UK last year after porn sites were required to start checking the age of visitors to comply with the Online Safety Act.