The Scottish vote came as Ms May's cabinet subcommittee on Brexit met amid enduring differences over Britain's customs relationship with the European Union after Brexit.
Mr Russell will now write to David Lidington, Theresa May's de facto deputy, who has been leading talks with the devolved administrations for the UK. Adam Tomkins, the ScottishConservatives' constitutional spokesman, said: "It's patently obvious that Nicola Sturgeon wants a political crisis to provide cover for her independence drive".
ScottishFirst Minister Nicola Sturgeon told a discussion at Thomson Reuters in London, she believed the United Kingdom was at a juncture when it could face a softer Brexit or a "no deal" Brexit, despite no majority for a hard Brexit in the country.
The SNP, Labour, the Greens and the Liberal Democrats all voted against consent, with only the Scottish Conservatives arguing the changes that have already been made to the bill go far enough to protect devolution.
The Welsh deal in turn led the House of Lords to endorse the United Kingdom stance, increasing the likelihood the measures will be passed by the Commons.
Months of negotiations has seen some agreement, and the ScottishGovernment are happy with the idea of common frameworks, but as long as Holyrood has the ability to accept or reject them.
No. When the UK Government was taking welfare reforms through Parliament, MSPs withheld consent for part of this legislation.
Speaking in Holyrood, he said: "While the UK Government is delivering additional devolution".
Such a move would not prevent the UK Government from introducing the legislation - but it would be the first time Westminster has pushed through laws against the wishes of the Scottish Parliament.
"There is a clear solution which is, as I have said and as the committee agreed last week, to simply remove [clause 15] from the bill".
He added the Tories' "shambolic handling" of matters meant the issue could be resolved in the Supreme Court - where judges will rule if the Scottish Government's alternative Continuity Bill falls within Holyrood's legislative competence. "I hope the UK Government will make this simple change before the legislation is passed and respect the devolution settlement Scotland voted for".
"There is a real risk of a no deal Brexit and that would be pretty catastrophic", Sturgeon said.
"There will be different opinions as to whether we should do that now or in five years or ten years' time, but with that body of opinion, a constitutional option like independence is not going to be off the table", she said. Nicola Sturgeon has refused to compromise.