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Theresa May’s approval rating has plunged to a record low with many voters rejecting her Chequers Brexit plan, an exclusive poll for the Evening Standard reveals today.

Less than one in three adults are satisfied with the job she is doing as Prime Minister, down five points on June to 30 per cent after an explosion of Tory infighting over Brexit.

The Ipsos MORI survey showed an even sharper fall in this satisfaction rating among Conservatives, plummeting from 68 per cent to 55 per cent.

The poll, carried out after the Chequers Brexit deal which angered many Tories and saw Boris Johnson and David Davis quit the Cabinet, found even less contentment with the Government, just 22 per cent.

But despite Mrs May facing the threat of being toppled in an autumn Brexit bloodbath, Jeremy Corbyn is plumbing similarly dismal approval depths, possibly even worse.

His satisfaction rating has fallen from 31 per cent last month to 28 per cent and more than half of adults think Labour should ditch their leader before the next general election, up from 43 per cent in September to 55 per cent.

This figure includes 37 per cent of those who support Labour which has failed for months to deal with a raging anti-Semitism row.

Mrs May fares slightly better, with 46 per cent saying the Conservatives should switch leader before the planned 2022 poll, including 34 per cent of Tory backers.

The Prime Minister was due to hold talks with the Austrian Chancellor Sebastian Kurz and Czech counterpart Andrej Babis in Salzburg today, just a day after EU chief Brexit negotiator Michel Barnier blew a hole in her Chequers plan by rejecting her “facilitated customs arrangement” proposal for Britain’s borders.

Cabinet ministers are touring EU cities seeking to persuade national governments to take a more flexible approach than Mr Barnier on Brexit.

However, Czech European affairs minister Ales Chmelar insisted Mrs May would struggle to find “loopholes” in the EU’s approach - and predicted Britain would suffer far more from crashing out of the EU with “No Deal”.

“The EU is roughly population-wise eight times bigger than the UK,” he told BBC radio.

“So...the relative impact on the UK might be as large as eight times larger than on the EU.”

MEPs also threatened to torpedo the final Brexit treaty unless the Government bends in the row over the future of the border between Northern Ireland and the Republic.

Lead Brexit MEPs, led by Guy Verhofstadt, said that UK backtracking on a “back-stop” arrangement for the border could “undermine trust and sabotage negotiations”.

The grim results for both Mrs May and Mr Corbyn appear to be driven by growing disquiet and hardening attitudes over Brexit and gloom over the short-term economic prospects.

Nearly half of people believe the Chequers deal will be bad for Britain, with just 29 per cent expecting it to be good.

Slightly fewer people now believe the economy will improve over the next 12 months, down from 19 per cent in June to 17 per cent, with those believing it will get worse unchanged at 54 per cent.

Gideon Skinner, head of political research for Ipsos MORI, said: “Theresa May has faced a lot of criticism since she launched her Chequers deal, and our poll for the Standard shows this is mirrored among the public, with her ratings continuing their recent decline to another new low.

“But despite all that, our trends show her ratings are not unusual for a Prime Minister two years in, and are still better than many of her potential alternatives.”

Just a quarter of adults are now confident Mrs May will get a good deal in negotiations with other EU leaders, a record low.

However, she still remains more trusted than other prominent Westminster figures to make the right decisions for Britain on quitting the EU.

Just over 40 per cent have confidence in her to do so, compared to 35 per cent for Mr Johnson, 33 per cent Chancellor Philip Hammond, two points more than Mr Corbyn, with Brexiteer Jacob Rees-Mogg on 29 per cent.

Nearly three quarters of Tory supporters back her to do the right thing on Brexit, far more than Mr Johnson, Mr Hammond or Mr Rees-Mogg who are all below half.

With Mrs May possibly facing a vote of no confidence in the autumn, twice as many Tory backers still believe she has what it takes to be Prime Minister than Mr Johnson, 63 per cent compared to 31 per cent, with new Foreign Secretary Jeremy Hunt on 22 per cent, Home Secretary Sajid Javid on 18 per cent and Environment Secretary Michael Gove on 14 per cent.

A third of adults believe the Conservatives have the best Brexit policies, only a fifth say Labour, a tenth the Liberal Democrats, followed by “none” of the parties on nine per cent, a sign of voters’ exasperation at politicians’ handling of the issue.

The headline voting figures show the Tories and Labour neck-and-neck on 38 per cent, with the Conservatives down three points on June, Labour unchanged, the Lib-Dems, up three points on ten per cent and Ukip up two points to six per cent.

Lib-Dem leader Sir Vince Cable’s satisfaction rating fell three points to 24 per cent.

* Ipsos MORI interviewed 1,023 adults between July 20 and 24. Data are weighted.