Parker's comments come ahead of a vote at the UK House of Commons later in the day on the government's Brexit agreement.
"I do not trust the Prime Minister on this and it just kind of looks like the last dash with a lot of drama. It felt very stage managed. It's still a bad deal and nothing has changed. The government and the shenanigans of the prime minister have left people wringing their hands. They’re thinking 'we see through this' and they are fed up," Parker, who is also a deputy chairperson of UKIP, said.
The lawmaker stressed she was seeing more and more people who think the United Kingdom should be out of the European Union, on its own terms, on March 29, as scheduled, "because we feel we'll have a better deal, with a more level playing field with the EU after we've gone."
"So, as far as I can see that's still on the table. It's a strong card. Yes, of course, we'd love to leave with a nice deal, but because [May has] given so much away and spent so long at it people have lost faith. They are fed up… If we leave on [World Trade Organization] WTO terms, the world will not collapse. It will be a bit rocky but we'll survive it and end up with very good deals with the EU, I believe that," she pointed out.
Parker added that the concerns expressed earlier in the day by UK Attorney General Geoffrey Cox that the backstop mechanism retained a "legal risk" of entrapment were well founded.
The lawmaker argued that even the withdrawal with May's updated deal would likely involve the United Kingdom being trapped in a "no man's land" with little option for manoeuvre.
"I think that the attorney general is an honest man. He's been straight forward on this. We stand to be trapped in a no man's land for however long. The electorate has been very forgiving but here we are on the front line dealing with issues like homelessness, lack of police, knife crime, so they are pretty fed up," Parker underlined.
Following the talks in Strasbourg with European Commission President Jean-Claude Juncker, May said on Monday she had obtained "legally binding" assurances that any backstop would remain temporary until a suitable UK/EU trade deal could be negotiated.
However, doubts started to appear on Tuesday when Cox stated the updated backstop retained a "legal risk" given the arrangement still apparently lacked any "internationally lawful means of exiting the Protocol’s arrangements, save by agreement."
May's predicament appeared to become yet more dangerous following the emergence of renewed opposition from the eurosceptic European Research Group (ERG) as well as key allies in the Democratic Unionist Party, with the prime minister seen as being likely to endure another defeat in the House of Commons.
According to Parker, a possible solution might be found if May resigned her position, with an ultimate no deal Brexit likely to be "rocky" but tenable.
"She needs to go quite quickly. We should have an interim prime minister until they can run proper elections but if you really want to get on and do something dynamically you have to do this. I'm not sure what she'll do but I hope she stands down quite soon," Parker argued.
If the government's deal is not passed on Tuesday, a vote on a no-deal scenario is expected to take place on Wednesday. If that is rejected as well, a vote on extending the Article 50 period will be held on Thursday. At the moment, the United Kingdom is expected to leave the bloc on March 29.
The views and opinions expressed by the lawmaker in this article do not necessarily reflect those of Sputnik.