Ministers may be forced to make significant concessions on a string of flagship government bills to get them through the current session of parliament, it has emerged, amid an increasingly tight legislative logjam. The government has already written to peers saying it will give ground on a key part of its controversial elections bill before it is scrutinised by the House of Lords, in an attempt to get it into law before the Commons is prorogued, expected to happen later this month. The letter, from Cabinet Office minister Lord True, said the government would not pursue a change in the rules over third-party campaigning, one which Labour had warned could severely affect the ability of trade unions to assist the party. Peers could now seek concessions on other contentious elements of the elections bill, including rules requiring photo ID for voters and closer ministerial control of the Electoral Commission. Adding to the time pressure, two other major bills are still being examined by the Lords, and might require amendments if they are to pass in time: the police and crime bill, and the nationalities and borders bill. Peers have already heavily amended both, removing planned powers to clamp down on the right to protest from the police and crime bill, and overturning a series of measures in the borders bill, including the idea of sending asylum seekers who arrive in the UK to overseas camps. Labour’s leader in the Lords, Angela Smith, said there was a wider issue with the sheer scope and drafting of bills like those on policing and on borders. “When there are that many amendments, maybe it’s time for them to be thinking: ‘Hang on, should we be doing all this?’” she said. “We’ve got two massive bills that are hugely controversial, they weren’t properly sorted out before they started, and the government wonders why it can’t get them through.” While, under convention, the Lords is expected to give way if MPs make it plain they do not back amendments from peers, the sheer lack of remaining time means a miscalculation by ministers could see one or more bills falling. Bills can be carried over to a new session of parliament, but not if they have already been considered by both chambers of parliament, which is the case for these bills. On Thursday the Commons leader announced that three other bills, which are eligible for carry-over, will see this happen: a controversial bill about freedom of speech in universities, an animal welfare bill, and a bill about high speed rail. The state opening of the next session of parliament has been announced for 10 May. While the date for the prorogation of parliament, ending the current session, has yet to be announced, it is expected to happen on 28 April, so MPs can return to their constituencies for local elections on 5 May. This leaves very little time for legislative business to be completed. The Commons goes into Easter recess for a fortnight on Thursday, with the Lords taking a two-week break one week later. The staggered recess times means there could be just one week, starting 25 April, when both houses are sitting before prorogation. According to figures compiled by the Hansard Society parliamentary thinktank, of 26 bills announced at the time of the last Queen’s speech a year ago, only 11 have so far received royal assent, although about 11 more could do so in the coming weeks. The pressure on parliamentary time has been exacerbated by nine extra policy bills being introduced beyond the Queen’s speech, such as the rushed-through economic crime bill, which assisted with imposing sanctions on Russia. On the elections bill, many peers had expressed serious concerns about its constitutional implications and “have a strong negotiating hand”, said Ruth Fox, director of the Hansard Society. “There are still several legislative stages left and they can send lots of amendments back to the Commons. But they also know they will be wading into treacherous constitutional waters if they effectively block a Queen’s speech bill passed by the elected house.”