In a letter his constituents in Tatton in Cheshire, the former chancellor said he was "very excited" about the prospect of editing the paper.
Prior to today's announcement, the HE Bill had been expected to return to the House of Commons for consideration of amendments at around 25 April. "The public want us to deliver on leaving the European Union and they want us to build that stronger Britain for the future beyond leaving the European Union".
A BBC spokesman said it was too early to say whether the broadcaster would seek to stage a debate.
Sir Vince, who served as former business secretary in the coalition government from 2010-2015, is one of a batch of Lib Dems who have confirmed they will stand again in the upcoming election.
Speaking outside Downing Street after officially taking up the position of Prime Minister in July of previous year, Mrs May praised her predecessor, David Cameron, for his legacy on issues including same-sex marriage.
Mrs May told MPs: "There are three things a country needs, a strong economy, strong defence and strong, stable leadership".
"There's so much more to come and as the party comes together to campaign for these popular polices, we are convinced our support in the polls will increase".
Mr Corbyn has led Labour since September 2015, and he was re-elected last September, winning the votes of almost 62 per cent of the party's membership.
It will also be hard to unseat Mr Corbyn in an internal election for party leadership if he continues to enjoy widespread support among the membership.More news: Fox kicks Bill O'Reilly to the curb
But current opinion polls suggest that Mrs May will lead her party to a position of greater strength in parliament, and that Labour will suffer deep losses. Explaining her change of heart for an early election, May said: "I have concluded the only way to guarantee certainty and security for years ahead is to hold this election".
"Why are so many people getting poorer?"
But Labour MP Gisela Stuart, one of the architects of Brexit as co-chair of Vote Leave, said she would be standing down after 20 years as MP for Birmingham Edgbaston.
"A stronger economy, an economy with the deficit almost two-thirds down, with 30 million people with a tax cut, four million people taken out of income tax altogether, record levels of employment and £1,250 more a year for pensioners. Since the referendum, we have seen consumer confidence remain high, record numbers of jobs, and economic growth that has exceeded all expectations".
Dugdale's plea for voters "sick to the back teeth" of debating the constitution to back her party was understandably overshadowed by May announcing an intense 50 days of debating the constitution.
In Bolton, Mrs May said the country now has a "unity of purpose" and a desire for the Government to "get on" with implementing Brexit and "making a success of it".
"Austerity has failed", he said.
Later, at Prime Minister's Questions, Theresa May tackled another Labour MP quizzed on the same topic.