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Prime Minister Theresa May is under no obligation to amend her Brexit plan if Scotland objects, but experts warn that a confrontation between London and Edinburgh could push Scotland towards independence.

Bruce Crawford, the head of the Parliament's Finance and Constitution Committee, said the vote was a "historic and significant" moment for Scotland and that he hoped the government in London would "respect the views" of the assembly.

British Prime Minister Theresa May said on Wednesday she was disappointed by the Scottish parliament's decision to refuse consent for the flagship legislation which will end Britain's membership of the European Union.

Scotland voted on independence in 2014, before Brexit.

"We are likely to be joined by Labour and the Liberals and the Greens in the Scottish Parliament so it will only be the Conservatives that vote to go ahead", she said.

The Scottish government has urged the parliament in Edinburgh to refuse "legislative consent" for the highly contested European Union (Withdrawal) Bill now being debated by lawmakers in London.

Scottish secretary David Mundell said that, although Tuesday's refusal of consent for a Westminster Bill was unprecedented, the 1998 devolution legislation envisaged such a situation.

"The danger if I am being less optimistic, or pessimistic, is that the whole process crashes before [a deal] can emerge because time is running out and the clock is ticking", Sturgeon said on Monday.

The Welsh government has agreed the United Kingdom government has the final say if there are disputes in the five years from Brexit day over these policies, after ministers in London amended the European Union bill in response to Welsh and Scottish concerns.

"The Scottish issue is just one among many headaches", Akash Paun, senior fellow at the Institute for Government in London told Bloomberg. "It becomes a bigger issue at the point when the bill is completing its passage through Westminster".

At issue is a bitter dispute between Westminster and Holyrood over powers now held by Brussels, which the SNP wants devolved after Brexit.

Meanwhile, 30 lawmakers supported the proposals on post-Brexit power sharing. Now she's at risk of having to impose British sovereignty against the will of the Scottish Parliament unless there's a compromise on what the Scots are calling a "power grab".