In June 2016, when the country held a referendum on Britain’s EU membership, the option to leave seemed very attractive to many. Severing links with the EU would mean breaking free, saving money, winning back independence. It would be all gain and no pain. But crucial information on what Brexit would mean was not available to them then. It was like being given the chance to buy an attractive house in the country without being told the price. Soon we will know what that price is. Then it may be that the house does not seem quite as attractive as once it appeared

On Tuesday, the Lords begins its consideration of the EU withdrawal bill. One of the big questions the upper house faces is: does it have the constitutional right to attach an amendment requiring a referendum on the terms of exit, before Britain finally leaves the EU? In other words, has it got the ability to push for legal changes that would allow voters to think again once they know as much as there is to know about the deal?

There are certainly precedents for such a course. Not only that, but it may just be, down the line, that this government, which currently insists it is totally against such a move, might find that such a vote is in its own interest. In 1985, an independent peer moved an amendment providing for a referendum on the London government bill, abolishing the Greater London council, while in 1993 Lord Blake – Robert Blake, the Oxford constitutional historian – moved an amendment, supported by Lady Thatcher, providing for a referendum on the Maastricht treaty.

Although both were defeated, hardly any peers suggested the Lords were acting unconstitutionally. Indeed, Lord Wakeham, leader of the house in 1993, said: “It is perfectly within the rules and conventions of this house for your lordships to seek to ask the other place to think again on this issue.”

What would not be in order would be for the Lords to insist on a referendum amendment if the Commons rejected it. The current parliamentary session is, on present expectations, to last for two years and so, if the government had to use the Parliament Act to pass legislation over the head of the Lords, the withdrawal bill would not be on the statute book before 29 March 2019, when Britain is due to leave the EU. With EU legislation not incorporated into the statute book, the outcome would be a legal vacuum, if not legal chaos. The Lords, therefore, can legitimately ask the government to think again. What it cannot do is to block the legislation.

The situation with regard to Brexit is, however, crucially different from what it was in 1985 or 1993. For the decision to leave the EU was made, not by government or the Commons, both of which contain a majority of remainers, but by the people in a referendum, who issued an instruction to government and parliament. The Parliament Act of 1949, limiting the powers of the Lords, makes no provision for such a situation since it was passed before referendums had become effectively part of the constitution. Nevertheless, by analogy, if the Lords has the constitutional right to ask the government and the Commons to think again, surely it also has the right to ask the sovereign people to think again.

Of course, as matters now stand, the government and the Commons may well reject a referendum amendment. Yet, ironically, a referendum could prove a lifeline for the government. Theresa May is engaged in a difficult negotiation with the EU. It is in the nature of a negotiation that one rarely achieves all that one wants. Whatever the terms, Jeremy Corbyn will say that Labour would have done better. Tory Brexiters will cry that too much has been given away, while Remainers will argue for a closer relationship with the EU. There could be deadlock in the Commons, while the resulting Tory recriminations could make the squabbles over Maastricht resemble a vicarage tea party. But if the Tories were to vote the deal down, the government would resign and Corbyn could enter Number 10. A referendum, therefore, might prove more attractive to Conservatives than voting for an unpalatable deal.

The government dare not commit itself to a referendum now or the EU would deliberately negotiate stiff terms in the hope that Britain would reject them and remain in the EU. So, for the Tories, the referendum is for the moment the love that dare not speak its name.

But, above all, the people have a right to vote on the framework of the deal once it is known. The 2016 referendum cannot be definitive. The cabinet and Tory party are divided on what the right price should be. But these divisions reflect a divided country. If the country is willing to pay the price, a referendum would legitimise Brexit in the only way possible. If it is not, the people have a perfect right to change their mind. A sovereign parliament, it is often said, cannot bind itself but nor, surely, can a sovereign people; and, as David Davis, the Brexit secretary, reminded us. “If a democracy cannot change its mind, it ceases to be a democracy.”

Vernon Bogdanor is professor of government at King’s College London. His books include The New British Constitution