Ahead of the meeting, the committee chairman Sir Graham Brady met privately with the Prime Minister in Number 10.
Under the current Tory party rules, MPs can not mount a new leadership challenge until 12 months after last December's failed attempt.
"In remarks that betray the loss of obviously conservative figures away from the increasingly centrist Tory party, the former party leader said: "[Widdecombe is] incredibly popular among grassroots Conservatives and I also think she's pretty popular among the public...
She said: "I'm afraid the prime minister is conducting negotiations in such a way that the party does not approve". "I think lots of people thought that was great and I think she's a formidable force". "He has gone from his death bed to the Olympics, because Brexit hasn't happened".
But following the latest extension to the Article 50 withdrawal process there is growing impatience among her critics.
The former shadow home secretary will now face off against Boris Johnson's journalist sister Rachel, who is a Change UK candidate in the South West.
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Opinion polls suggest that the Brexit Party could be set for a good result in the European Elections - it has been formed with the sole aim of pulling the United Kingdom out of the EU and has attracted the support of most of those voted to Strasbourg under the UKIP banner five years ago.
It is thought that it may seek to accelerate progress by tabling the Withdrawal Agreement Bill (WAB) in the Commons as early as next week, even if cross-party talks have not reached a conclusion. Most of the recess was consumed with talk of plots to unseat Prime Minister Theresa May rather than how to resolve the current Brexit impasse.
"We can't continue as we are just sat waiting for something to emerge".
On Whitehall, the Conservative and Labour Brexit talks started again after the Easter break.
May has said she will step down if her Brexit deal, which has already been rejected three times, is passed by parliament but has not set out what she will do if it is not.