Mr Blackford tried to use an arcane procedure demanding the "House sit in private" - a motion that requires a vote of MPs on whether to clear public galleries.
"I have a duty on behalf of my colleagues, on behalf of the First Minister and the government of Scotland and of the Parliament of Scotland, to stand up against the betrayal that has taken place of the Scottish people with the unprecedented power grab which is taking place". Blackford told BBC News afterwards that he was within his democratic rights to call for an immediate vote within the House, and the walk out was in protest against "the complete disrespect".
The SNP MP told the same programme: "He ought to resign and the fact we have seen powers taken from the Scottish Parliament and our elected representatives have not been able to debate this is an utter, utter disgrace".
But MSPs at the Scottish Parliament refused to give their blessing for May's Bill - something Blackford says has been ignored.
But Theresa May retorted: "We do expect that the outcome of Brexit will be a significant increase in Holyrood power".
His actions today were as a direct result of the democratic outrage in the House of Commons last night, as the Tories' power grab on devolved administrations was not debated in the chamber, and Labour abstained on a devolution amendment in a shocking dereliction of duty.
He then demanded a vote on the issue, something which Bercow refused to consent to until PMQs had concluded.
Scottish Secretary David Mundell said the SNP was about to be granted a debate on the devolution aspects of the EU Withdrawal Bill by the Government.
He was followed by some 30 of his SNP members.
"The Prime Minister gave a commitment that she would treat Scotland as part of a "union of equals".
"We hear from the Prime Minister about respecting devolution. Not one single Scottish MP was able to speak in that debate", he added.
While Conservatives at Westminster say some of these must come to Parliament to allow for common frameworks to be established in areas such as agriculture and environmental regulations, ministers at Holyrood fear the powers of the Scottish Parliament could be restrained for up to seven years.
SNP leader Nicola Sturgeon has said she was "right behind" Blackford and accused Westminster of treating Scotland with "contempt".