The Bill, called by Conservative MP Chris Skidmore, would mean that if an MP decided to switch their party political affiliation an automatic by-election would be triggered so that their constituents would be able to have the final say.
The Kingswood MP said that there had never been a debate on the issue, and his suggestion would overturn 'centuries of tradition', adding that it is the honest and right thing to do.
Steve Brine added: "I was very much in favour of Chris' Bill today. It is wrong that at present a by-election is only called if the MP chooses to resign, and this would be the right approach in ensuring constituents are truly represented."
After passing through the first reading stage, Mr Skidmore's Bill now joins the queue of Private Members' Bills waiting for a second reading, which will be on will be on March 16, 2012.
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You can read what happened on Hansard here.