So far, the Prime Minister has admitted that there were "conversations" between senior Tory party members and the Brexit Party, but flatly denied that any peerage had been offered, saying that it was "just not the way we [the Tories] operate".
Arch eurosceptic Nigel Farage, who founded the Brexit Party earlier this year, has accused Prime Minister Boris Johnson's Tories of "corruption of the worst level" by offering his candidates jobs and peerages to withdraw from the Dec 12 election.
United Kingdom police have received two allegations of electoral fraud and malpractice concerning the December 12 vote.
Opinium surveyed 2,008 people online between November 13 and November 15, after the Brexit Party announced it would not stand in seats held by Conservative members of parliament.
Meanwhile, the MEP said he thinks staying in the European Union would be better than going ahead with Boris Johnson's Withdrawal Agreement.
"Both allegations are now being assessed", it said in a statement, noting its special enquiry team is responsible for investigating such cases.
He was also pressed on allegations the Conservatives have offered jobs and peerages in return for them standing down. Each allegations are at the moment being assessed.
Mr Farage has claimed he had repeatedly been provided a seat within the Home of Lords in an try to influence him to "go quietly".
Mr Lewis told Sky's Ridge on Sunday today: 'No-one has been offered jobs or anything like that. Absolutely. It has been going on.
Lord Falconer said: "These are exceptionally serious allegations which the DPP must, in accordance with his statutory duty, fully investigate as a matter of urgency".
And the Liberal Democrat president Sal Brinton has written to Conservative Party chairman James Cleverly calling on him to launch an immediate independent internal enquiry into "what dialogue, if any, Conservative Party officials have had with Brexit Party candidates and officials".
The Brexit Party leader had already said they would not contest the 317 seats which the Conservatives had won in the 2017 election.
"We are not forming coalition governments, we will put forward the programme on which we will have been elected", he said.
Lord Falconer's letter includes a mention of Ann Widdecombe, the former Tory MP now standing for the Brexit Party in Plymouth Sutton and Devonport.
Asked about the Conservative Party's denials, and whether his comments amount to saying the Tories are lying when they refute the allegations, Mr Habib said: 'I'm saying they're being economical with the truth for sure.
'Ann Widdecombe, for example, was offered some sort of negotiating position with the Tory Party, from Number 10, someone from Number 10 called Ann.