PRIME Minister Theresa May's Brexit plan must be backed or there will be "empty supermarket shelves", says Poole's MP.

Today, Brexit Secretary David Davis resigned from the cabinet over the Brexit plan agreed at Chequers on Friday, which he said was "giving away too much and too easily" to the EU in the negotiations.

But Poole MP Sir Robert Syms said achieving a deal with the EU was urgent.

"We have to go along with the plans, there aren't the votes in the House of Commons for anything other than something which finds a compromise," he said.

"We are running out of time and need to negotiate, those who will find themselves with empty supermarket shelves, being put on short time and standing in a queue at customs will be the first to moan.

"We do need a deal."

Sir Robert said the priority was to leave the EU "in an organised and orderly way" and that it could take "several years to disengage fully".

Prime Minister relying on 'bad advice'

However, Christchurch MP Sir Christopher Chope said the Brexit plan was "not taking back control" as it would mean British businesses having to abide by EU regulations even while trading outside the bloc.

He said it would likely be rejected by the EU.

"Theresa May has not been in charge so much as the establishment civil service, who have cooked this plan up," he said.

"You have got the people on one side and the unelected, unaccountable elite on the other side.

"Quite a lot of large multi-national companies benefit from the status quo and fear they would suffer from competition.

"She says she has a personal commitment to Brexit, but I think she has relied upon bad advice.

"The whole negotiation has been based on a stance of pessimism about our ability to get a good deal, that we have the begging bowl.

"In fact we have got the strong position.

"The EU supplies more stuff to us than we do with them, and has a lot more to lose if there is no agreement in place."

Sir Christopher said he was pleased the plan had come with a commitment to prepare for a 'no deal' situation under World Trade Organisation regulations.

"Most of us believe what is already on the table will be unacceptable to the EU anyway," he said.

What 'pragmatic' leavers wanted

North Dorset MP Simon Hoare said 'no deal' was not an option.

"That is what the business model is predicated on, what jobs are delivered by. If we have no deal we will have thrown the baby out with the bath water," he said.

"And if we can't negotiate a free trade agreement with our nearest neighbours and closest trading partners for 30 years what message does that send to the rest of the world."

He said the Prime Minister had his "unequivocal support" and described the plan as "common sense, pragmatic and realistic".

"It is good news for agriculture, it is good news for exporters, whilst continuing to deliver on the referendum decision," he said.

"If you talk to a lot of people who voted to leave a very common phrase is 'we joined the EEC for trade, we didn't vote for all the political baubles'.

"The political baubles are being cut out, this is a free trade deal with the EU.

"For pragmatic people who voted leave, this is what they wanted."

Johnson and Gove 'should resign'

Meanwhile the Brexit-backing managing director of REIDsteel in Christchurch, Simon Boyd, has urged cabinet ministers including Boris Johnson and Michael Gove to follow David Davis' example and do "the honourable thing".

“When Theresa May unequivocally declared in her Lancaster House speech that we would be leaving the single market, customs union and jurisdiction of the European Court of Justice we applauded her support for the Brexit the British people voted for," he said.

“With David Davis’ resignation in the wake of last Friday’s cabinet meeting at Chequers, it is time to stand shoulder to shoulder and fight for the Brexit this country must have if we are to realise the ability to strike our own trade deals and be free to regulate in the interests of British businesses.

“This supposed agreement, sells us down the river and it is a betrayal of the democratic will of the people.

“I applaud David Davies, Steve Baker and Suella Braverman for doing the honourable thing and resigning. I urge others in the cabinet, including Boris Johnson and Michael Gove, to do the same with immediate effect rather than put career above national interest."

He said the plan would leave Britain as "a de facto member of the EU" and was "a kick in the teeth" for the British people.

“Many in business who voted to remain have now come to realise that we must have a clean Brexit to claim the freedom to make our own trade deals on the world and restore the primacy of British Standards away from the plethora of damaging EU directives and regulations."