The ex-chair of the all-party parliamentary group for Russia called into question whether the 55-year-old oligarch should be allowed to maintain his ownership of the Premier League club after the invasion began.
He revealed that a leaked Home Office report named Abramovich as a person of interest to the government amid reports of his links to Vladimir Putin – which he denies.
On Saturday night, the Chelsea chief announced he was stepping back and handing over his “stewardship” of the club. However, Bryant believes that should not relieve him of pressure over his alleged links to the Kremlin.
“I’m worried that the British press (with some notable exceptions) have fallen for the Abramovich line on ceding control,” he tweeted.
“Unless and until he condemns the criminal invasion of Ukraine I will continue to call for the UK to sanction him and seize/freeze assets.”
Chelsea released a statement on Sunday morning calling for peace in Ukraine, while not explicitly condemning Russia or president Putin.
It read: “The situation in Ukraine is horrific and devastating. Chelsea FC’s thoughts are with everyone in Ukraine. Everyone at the club is praying for peace.”
Abramovich’s daughter, Sofia, made headlines in the week by posting an anti-Putin message to her social media.
The Chelsea Supporters’ Trust are seeking “urgent clarification” on what the Russian stepping back from his role means in terms of the club’s future.