Jeremy Hunt admitted that article 50 may have to be extended to avoid the UK crashing out of the EU without a deal on 29 March, earning him a rebuke from Downing Street even though his comments were technically correct.

The foreign secretary, speaking to the BBC Radio 4’s Today programme, conceded that a delay might be necessary if an agreement with the EU was reached just days before the March deadline – although the prime minister has consistently ruled out seeking any extension.

Asked if a technical delay would be necessary, Hunt said: “That depends on how long this process takes. It is true that if we ended up approving a deal in the days before the 29 March, then we might need some extra time to pass critical legislation. But if we are able to make progress sooner then that might not be necessary.”

At a Downing Street briefing, when asked about Hunt’s remarks, the prime minister’s spokesman asserted: “The prime minister’s position on this is unchanged. We will be leaving on 29 March.”

The prime minister’s spokesman added that ministers were “absolutely determined” the Brexit deal be completed on time, which was why MPs had been told that the February half term recess would almost certainly be cancelled.

Insiders suggested that the foreign secretary’s remarks were unhelpful, although they appeared to be accurate because there will come a point in March where it will no longer be possible to ratify a deal in time for the end of the month.

Any Brexit deal has to be approved by MPs in a future meaningful vote, and ratified by the passing of a withdrawal agreement bill. There is no firm date for a second Brexit vote, although May is currently aiming for 14 February – but that could slip further.

Downing Street estimates suggest that the ultimate deadline for striking a Brexit deal with the European Union could be as late as mid March, which would be in line with Hunt’s comments.

Whitehall sources say they believe the complex legislation could be got through parliament in around a fortnight, while some of the six other Brexit-related bills going through parliament could be delayed until after 29 March.

Speaking ahead of an informal summit with his EU27 counterparts in Romania, Hunt described the Brexit impasse as “a very challenging situation”. Hunt claimed changes to the withdrawal agreement could be made if the UK could allay Irish fears about a possible hard border and those of the wider EU about the integrity of the single market.

He said: “Provided we can meet these very reasonable concerns from our friends in Ireland about not having a hard border and concerns in the EU about access to the single market – provided we can do that, which I think we can, then I think there is a way through.”

He played down the insistence in Dublin and Brussels that negotiations on the withdrawal agreement would not be reopened.

Hunt said: “These are negotiations. People’s first reaction when you make some new proposal to break a deadlock is to say ‘no, no, no that’s completely impossible’, but in reality the EU said to us: ‘Tell us what parliament can unite behind’ – we’ve done that. Secondly, we will now put together some proposal that makes sure we don’t breach these two very important principles for the EU.”

May has no plans to travel to Brussels or elsewhere in Europe until early next week at the earliest. Senior ministers expected the initial reaction of the EU and its member states to be hostile, but hope that once the mood has calmed somewhat it will be possible to negotiate.

Hunt also said Crawford Falconer, the chief trade negotiator at the Department for International Trade, would not be added to the team leading the negotiations with Brussels, despite assurances given to Brexiter MPs.

Hunt said: “To my knowledge there has not been a change in the team.” But he added: “I’m sure we are going to tap into his brilliance. He’s an extraordinary man and a very, very experienced trade negotiator … I would be very surprised if he wasn’t feeding into the process.”

He also admitted that the business secretary, Greg Clark, was wary of technical alternatives to the Irish backstop put forward in the so-called Malthouse compromise.

“We are not looking at one particular solution which is the only way forward,” said Hunt. “There was a consensus in the Conservative parliament party around a technology solution put together by Kit Malthouse. That is one of the things we are looking at. He [Clark] had some scepticism about it.”

Pressed on what “alternative arrangements” the government would be proposing to the EU, Hunt said: “We have put these proposals together, we have to work them up, we have to go through them in detail with our partners in the EU … It is going to take a few days to do that, but we are not going to spell those out on air.”