Laird offered to arrange for parliamentary questions to be asked in return for a fee of £2000 ($3821) a month.
Clegg says the Government will now introduce laws to create a statutory register of lobbyists and give constituents the "powers of recall" to force a byelection if an MP engages in serious wrongdoing.
On taking office, the Coalition promised to create a statutory register of lobbyists, to ensure the industry was regulated. Clegg says he and Cameron are "determined that the register should go ahead" as part of a broad package to clean up politics.
Many Liberal Democrats blame Cameron's party for blocking action on lobbying.
A peer embroiled in the growing parliamentary lobbying scandal has resigned from his party.
A separate investigation into lobbying by the Sunday Times has also led to two peers being suspended from the Labour Party over claims they offered to carry out parliamentary work in return for cash. Lord Cunningham, a former Cabinet minister, and Lord Mackenzie, a former senior police officer, are alleged to have told reporters representing a fake solar energy firm they could help push its agenda, in an apparent breach of the strict ban on paid advocacy in Parliament. Cunningham said the report was "misleading" and he was taking legal advice. Mackenzie denied wrongdoing.