Nearly two thousand people in Hinckley and Bosworth have already signed a petition to save cheques.
Petition organiser, Liberal Democrat parliamentary spokesman for Hinckley and Bosworth, Michael Mullaney said "The response so far has been fantastic. We have been having petitions pouring in every day.
"In a few weeks time we will be sending all the petitions to the Prime Minister, urging him to support a parliamentary bill forcing the banks to continue issuing cheques. We want to send as many petitions as possible and I would urge residents who haven't yet signed to support the petition."
The petition can be signed online at www.bosworthlibdems.org.uk
The Liberal Democrat leader of Hinckley and Bosworth Borough Council, Stuart Bray, is aiming to get the support of the Borough Council for the campaign when he tables a motion about it at Thursday's Full Council meeting.
Cllr Bray said "We've had local housebound pensioners and their carers backing the petition. They've told us that scrapping cheques would take away one of the few bits of independence they have. The ability to write cheques to pay the plumber, or the handyman or to send gifts to their grandchildren.
"Community groups, church groups, sports clubs in the Hinckley and Bosworth area have written in saying that scrapping cheques would be a big inconvienience for their organisations.
"Small business owners have told us that it would damage their business if cheques were scrapped.
"I hope the government will listen to local people and force the banks to continue issuing cheques".