"If this Government forces through the legislation without the consent of the Scottish Parliament, the Prime Minister will be doing so in the full knowledge that they're breaking the 20-year-old devolution settlement", Mr Blackford added.
Scottish First Minister Nicola Sturgeon, leader of the separatist Scottish National Party, said Britain is now heading into "uncharted constitutional territory" with a majority in Scotland's semi-autonomous legislature expected to oppose the bill. The U.K. can disregard the vote, but it would be the first time London asserts its dominance over the regional parliament.
Mr Leonard, speaking on BBC Scotland's Sunday Politics Scotland programme, said: "As there appears to be a breakdown in trust between the two governments, there really needs to be an alternative way found forwards".
"The Government has completely redrafted this bit of the Withdrawal Bill in order to accommodate the sensitivity that actually these powers will, in the end, come to the Scottish Parliament". With the support of Scottish Labour, the Liberal Democrats and Scottish Greens, her government refused to give the European Union bill its legislative consent in the vote on Tuesday.
The dispute centres on who will have control of powers now residing in Brussels, such as over farming and fisheries, once Britain leaves the EU.
It has never been done before by the devolved Parliament in Holyrood.
The prime minister briefed Conservative backbenchers on Monday about the two options her ministers are considering: a customs partnership which see Britain collecting tariffs on behalf of the EU; and a combination of technological and administrative measures created to diminish friction on a UK-EU customs border.
Lidington has said he is "open to suggestions that would improve the Bill" but has repeatedly refused to amend the legislation.
Britain as a whole voted in June 2016 to leave the European Union, but Scotland voted to remain.
"If the United Kingdom government wants to widen the discussions and we are agreeable on a way to do so, we could do so but I think it would have to be on the basis there was something worth working on and as yet I have not heard that from them or anyone else".
The Labour-run Welsh Government previously shared the position of Scottish ministers, but dropped its opposition following changes to the legislation.
Nicola Sturgeon's government in Edinburgh insists that Holyrood must explicity agree to any changes before they can take effect.