Mr Clarke takes a break between jobs
"A quarter of MPs are evidently too greedy, too bored or too arrogant to devote the time and energy to the job their constituents are paying them to do," Mr Bradley said.
Conservative Michael Fabricant dismissed Mr Bradley's bill as "a load of self-indulgent, unreconstructed, ill-thought-out tosh."
'Class warfare'
Mr Fabricant, who claimed he would not lose out personally if such a Bill became law, said Mr Bradley had not taken into account the type of work or the amount of time dedicated to it.
"It was just a catch-all Bill which had absolutely nothing to do with the workings of this House and absolutely everything to do with old-fashioned class warfare," he added.
Farmers
Geoffrey Clifton-Brown
Tim Boswell
Mr Bradley said MPs were paid as full-time professionals, earning three to four times the income of many of their constituents.
"If we cannot commit ourselves to our constituents and keep the faith of them, how can we expect them to place their confidence in us?" he asked.
The Register of Members Interests shows that nearly 24% of MPs - or 155 - have at least one other outside interest.
"How can a Tory frontbencher be doing his job when he has 16 directorships to nurture?"
"No self-respecting employer in our own constituencies would tolerate the kind of moonlighting which many members of this House go in for," said Mr Bradley.
Several MPs, such as former Tory minister Douglas Hogg or Labour's Bob Marshall-Andrews, can often be found in the court room pursuing their original career as barristers.
While others spend time on the family farm - another popular pursuit for sitting MPs.
Adverse publicity
Of the Conservatives, 66% of MPs admit to a substantial outside interest.
Journalist Boris Johnson drew criticism from some quarters when he refused to give up the editor's seat at The Spectator when he became Conservative MP for Henley.
Failed Tory leadership candidate and MP for Rushcliffe, in Nottingham, Ken Clarke, has also come under fire for his outside interests.
The former chancellor is among the most active MPs - outside parliament - with five company directorships and a contract to make regular appearances on financial television channel Bloomberg to his name.
His most well-known boardroom role, deputy chairman of British American Tobacco, has attracted adverse publicity after the firm became the subjct of a DTI investigation into alleged smuggling.
But he is also on the board of Independent News and Media and Savoy Asset Management, Alliance Unichem PLC, Foreign and Colonial Investment Trust and BAT's Formula One racing team.
Busier
Fellow backbencher Tony Baldry, who represents the safe Conservative seat of Banbury, in Oxfordshire, is even busier.
Mr Baldry finds the time to be on the board of eight companies in four countries, including an investment house in Saudi Arabia, a company in the Czech Republic which promotes classical music and a manufacturer of tyre monitoring technology.
He also describes himself as a practising barrister.
But even Mr Baldry's extra-curricular activities are dwarfed by shadow treasury spokesman and MP for Arundel and South Downs, Howard Flight, who lists 16 separate directorships, mostly in the field of asset management.
Magazine column
By comparison, just 8% of Labour MPs would fall foul of the Bill.
Former Northern Ireland Secretary Peter Mandelson is perhaps the most high-profile moonlighter.
Apart from penning a monthly column for men's style magazine GQ, Mr Mandelson was recently appointed to the board of a new advertising agency set up by Johnny Hornby, brother of Fever Pitch novelist Nick.
Former Paymaster General Geoffrey Robinson's outside business interests have landed him in hot water in the past.
Unusual pursuits
Among the more unusual activities listed in the register of interests, is Stratford-on-Avon MP John Maples role as a director of Agatha Christie Ltd.
On a more humble note, Nigel Evans, Conservative MP for Ribble Valley, is described as the owner of a "retail convenience store in Swansea".
Most MPs list "occasional journalism" or lecturing as outside interest, but this is seen as being part of their job and would not fall under the scope of Mr Bradley's Bill.
The Bill received a formal first reading on Tuesday but stands little chance of becoming law due to shortage of parliamentary time.