The annual running costs of the new-look mainly elected second chamber would rise by £13.6m by 2025, when the changes are due to be fully implemented.
Yesterday, the bill was laid down in parliament and Tory Prime Minister David Cameron urged supporters of reform to make the case.
Mr Cameron was responding to criticism from senior Tory backbencher Bernard Jenkin in Prime Minister’s Questions, who argued that the changes in the European Union should be a much higher priority for the government.
Mr Cameron said: “There are opponents of Lords reform in every party. But there is a majority in this house for a mainly elected House of Lords, and I believe there’s a majority for that in the country.”
In a concession to critics, ministers have scrapped plans for a salary of about £60,000 for members of the new Upper House.
The government instead wants them to be paid £300 for each day they attend – a maximum of about £45,000 a year.
However, the intended pay limit is not set down in the bill, which says it will be up to the Independent Parliamentary Standards Authority (Ipsa) to set pay levels and stipulates only that elected Lords members must not earn more in a year than an MP: currently £65,738.