Parliament is deadlocked. The Brexit tin can that has been kicked down the road since June 2016 is now lodged firmly in the machinery of Westminster, bringing parliament to a grinding halt. MPs cannot now agree on how we might get parliament and government working again.

The prime minister has delivered a plan for Brexit that she feels is the best our country can achieve, given the government’s red lines. I have no doubt that she is sincere in this. But this doesn’t create a majority in the House of Commons for it. Quite the opposite: any rational examination exposes the deal’s flaws when compared with either the reality of the status quo or how far short it falls of the leave campaign promises in 2016.

The Labour position is even more questionable. When the opposition front bench is able to agree on what it wants, it usually focuses on wishing to retain customs union access, with a voice at the table in Brussels – both unacceptable to our European neighbours, and not in practice possible legally.

I believe that it is important, now more than ever, that members of parliament engage in rational arguments, not in reiterating undeliverable wishlists. Thankfully, roads have opened that could lead us out of this Brexit crisis. One obvious solution, which is fast gaining support, is to hand the issue back to the country. I would add that we also need formally to take no deal Brexit off the table, because that way lies chaos and disaster.

Both of these would help to calm a crisis that is only set to grow, unless parliament can assert itself and decide on a way forward. Work is being done by all sides to understand how we might find our way through the current crisis, and the campaign group Best for Britain has set out four ways to secure a people’s vote in its recent publication Roads Not Yet Explored: Routes to a Final Say, to which I have contributed a foreword.

Brexiteers tell us (and hope) there simply isn’t time to have another referendum before article 50 expires at the end of March 2019. But this is simply not the case. The EU will give us the time if we want it. So long as there is political will to deliver a solution to the current impasse, there is a course of action available to us that means we will be able to check whether or not the will of the people has changed over time. To call this a subversion of democracy is utterly wrong. We will not be thanked by anyone for dragging the country out of the EU on a deal for which the public have shown no enthusiasm. For MPs that would be an abdication of responsibility.

Parliament voted for the public to decide the United Kingdom’s future relationship with the European Union. We should now ask the people whether the prime minister’s deal satisfies their hopes and demands, and if it does not, offer a viable alternative. Our country needs a rational outcome and, judging from the current situation, parliament is not capable of delivering it. We need to open the road for the people to finish, one way or another, the task they started in June 2016. Whatever the result, parliament must abide by it.

• Dominic Grieve is Conservative MP for Beaconsfield and a former attorney general