The Scottish Parliament's refusal to back the bill through a legislative consent motion will not legally prevent ministers from pressing ahead, and the lack of an agreement in Scotland comes after a deal was reached between Westminster and the Welsh Government last month.
The SNP's leader at Westminster, Ian Blackford, said the vote showed the Conservatives were "isolated and out of touch with the people of Scotland".
In fact, Theresa May has ignored the will of the Scottish Parliament before, refusing to grant a second independence referendum past year after MSPs had voted for it.
Speaking on TalkRadio, Mr Jenkin said: "There's something of a manufactured row here that, of course, the powers that we are talking about were held by the European Union and were never held by the Scottish Parliament".
The British government will press ahead with the EU Withdrawal Bill despite the Scottish parliament's decision to withhold its consent for the legislation.
The Guardian said Conservative Party sources suggested May is likely to push the legislation through the House of Commons without Scottish parliament's consent.
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Public talk of defying Brexit, though, dissipated after May's governing Conservative Party increased support in Scotland in last year's election, even as she lost her United Kingdom parliamentary majority.
"That is why I must recommend the Scottish Parliament votes against accepting the bill in its current form".
"I think this is a reasonable, a sensible way forward - the Welsh government, and now the Welsh Assembly including Labour and Liberal Democrat members of the Welsh Assembly, agree with that".
"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".
The Scottish Parliament passed its own version of Brexit legislation, called the Continuity Bill, in March by a margin of 95 to 32 to ensure it retains control of areas that are now devolved after Britain formally leaves the EU.
The UK government has published proposals that would see the "vast majority" of these 158 powers go directly to the Scottish Parliament after Brexit.
What are the consequences of the Scottish Parliament refusing its consent?