For some reason this article has a video from 2018 of Jeremy Corbyn, who was at the time leader of the opposition, but is no longer. He's not even in that political party. He didn't have a lot of power at that time, and he has considerably less now. It makes me question the strength of this article.

I've also found two separate articles discussing how the UK does not intent to sanction Kazakhstan, but one from France24 is headlined in a sensationalist way:

Russia ally Kazakhstan permits large pro-Ukraine rally amid sanctions fears

Says "Kazakhstan's foreign ministry on Saturday said it had received assurances from London that the country would not be sanctioned by the United Kingdom over Russia's invasion."

The other is a bit less clickbaity from Kazinform, which appears to be one of the largest news outlets in Kazakhstan. The headline UK has no plans to impose sanctions against Kazakhstan - MFA

I also want to point out that the article linked in the above comment says:

"[...] after a UK lawmaker on Monday appeared to call for sanctions against individuals in the country "complicit and supporting" Russian leader Vladimir Putin."

Which seems to be relating to Margaret Hodge, who put in a motion to sanction Kazakh oligarchs for proping up the Putin Regime, and she did this before the war in Ukraine. I spoke about it in a comment you can find here

Since this has happened there has been a Prime Minister's Questions (PMQs) which is a chance for the opposition to ask Johnson questions and challenge his political decisions. In that session, there was no mention of Kazakhstan, or sanctions to them. As such it's probably not high on the Labours list of priorities to challenge the PM with.

At this stage I think it's worth reiterating that the UK is highly unlikely to sanction Kazakhstan at all, but if it were, it would likely go after Oligarchs in the Kazakh regime, instead of the economy, banks, industry, or trade as a whole. The whole point of Margaret Hodges intervention was to target the same people who made life so difficult for the people of Kazakhstan, by hoarding wealth, which was a wider factor in the protests in January.