Danny Alexander, David Laws and Simon Hughes understood to make up rest of the foursome of unseated party figures who have rejected peerages

Four senior Liberal Democrat politicians defeated in the general election, including former business secretary Vince Cable, have turned down offers of a peerage from Nick Clegg in the dissolution honours list. It is understood that David Laws, the former education minister, Simon Hughes, the former justice minister, and former Treasury chief secretary Danny Alexander have also decided to reject a chance to sit in the House of Lords.

The Lords is likely to be a battleground for the government since the Conservatives do not have an overall majority in the upper chamber, even though in practice there are strict limits on how far peers can resist central planks of legislation agreed by the Commons. The Liberal Democrats currently have 101 peers, Labour 214, the Conservatives 224 and crossbenchers 178.

Hughes, a former deputy leader of the Liberal Democrats, who lost his Southwark and Bermondsey seat to Labour, told guests at a recent birthday party: “I don’t believe in an unelected second chamber. When you see the list I will not be on it. I am not going there.”

Cable is understood to be writing a sequel to his previous overview of the UK economy, The Storm. He was writing the book as business secretary, but it is now likely to be a much a more frank account of where he believes government economic policy succeeded or failed.

He is also not a man drawn to the prestige of a peership, normally travelling to work by tube rather than by government car.

Cable was surprisingly beaten in his Twickenham constituency, and if he had won might have stood for the party leadership at least to act as a caretaker to oversee the party’s regrouping.

Norman Baker, the former MP for Lewes and another former minister, has also let it be known that he is not interested in a peerage. In a statement to his constituents he said: “For my part I intend to return to being a private individual and to start the next phase of my life. I have no regrets at all, and if someone had told me in 1987 that the deal was that I would be a councillor for 16 years, council leader for six, an MP for 18 years, and a minister for four-and-a-half years, I would have said that that was a pretty good deal.”

Alexander had been tipped for a peerage as it was believed if he lost his seat in Inverness, Nairn, Badenoch and Strathspey he would be needed to help oversee coalition negotiations, although it would not have required him to hold a peerage for him to play that role. He now seems focused on battling the SNP in Scotland.

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The most likely Liberal Democrats to take a peerage are Sir Menzies Campbell, the distinguished foreign affairs specialist, and Alan Beith, the former chairman of the justice select committee.

Meg Russell, the leading academic on the House of Lords, points out that David Cameron would need to appoint just over 160 new Conservative members with no peerages at all for other groups to give the government a Lords majority.

Simply to outstrip other parties, 70 would be needed – a rate of appointment which would be completely unprecedented, and greeted with legitimate outrage. Large-scale Lords reform does not offer a way out either, as the Conservative manifesto explicitly stated that this was “not a priority in the next parliament”.

So at least in the short term, the government’s only practical option is to learn how to manage the chamber more or less as it is.

• This article was amended on 18 May 2015. An earlier version transposed the numbers of Conservative and crossbench peers.