Morsi's death in court has been widely blamed on the current Egyptian government, which kept him in solitary confinement and denied him access to adequate medical treatment while he was suffering from diabetes and kidney disease.
Chair of UK detention panel calls for Morsi probe
"Dr Morsi's death in custody is representative of Egypt's inability to treat prisoners in accordance with both Egyptian and international law," said Conservative MP Crispin Blunt.
He said Cairo "has a duty to explain his unfortunate death and there must be proper accountability for his treatment in custody".
"The only step now is a reputable independent international investigation," he said.
The UN human rights office has called for a similar inquiry.
Blunt chairs the Independent Detention Review Panel, a group of British MPs and lawyers who published a report in March 2018 into how Morsi was being treated in custody.
They concluded that the former president, who had a history of ill-health including diabetes, liver and kidney disease, was not receiving adequate medical care.
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They found that his detention "is below the standard expected by international standards for prisoners, and would constitute cruel, inhuman and degrading treatment".
In a statement on Tuesday, Blunt said: "We feared that if Dr Morsi was not provided with urgent medical assistance, the damage to his health may be permanent and possibly terminal.
"Sadly, we have been proved right."
He added that the panel had found that Morsi's detention conditions could meet the threshold for torture in Egyptian and international law.
"We found culpability for torture rests not only with direct perpetrators but those who are responsible for or acquiesce in it," he said.
Morsi was Egypt's first democratically elected president who was overthrown in 2013 after a year of divisive rule.
He was buried under heavy security in a dawn ceremony closed to the public and press on Tuesday after collapsing in a Cairo courtroom.
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