Yvette Cooper, MP for Normanton, Pontefract and Castleford, and other questioned Ms Patel in her role as Chair of the powerful Home Affairs Committee.
But Ms Patel said she would “not [...] speak about hypothetical situations right now” when asked about border checks between Britain and Northern Ireland, despite this being part of the agreement MPs have been asked to approve.
MP Stephen Doughty said: "With the greatest respect, this is not a hypothetical situation. This is what the Brexit Secretary has confirmed to a select committee in the House of Lords, and to myself and the chair of the Brexit committee on the floor of the House, that there will be exit checks required on goods transiting from Northern Ireland to GB, so within our own country.
"And I'm asking you, are Border Force officials going to be involved in that?"
Ms Patel replied: "We are not there yet, so this is the point to make, we are simply not there in that situation.”
Ms Cooper criticised Ms Patel and said she did not seem to have a “practical” plan, and she asked at what point in the next 14 months does a security treaty need to be agreed in order to get it ratified in time for December 2020.
She added the committee had heard evidence that it would take 18 months to get a security treaty ratified.
But Ms Patel said: "Well I will say again, that we are in the process, and as you would expect, these are discussions that are ongoing with our counterparts, with the [EU] Commission.
"And I myself have been in touch with the Commission in terms of that security partnership, that security relationship.
"And it's important that we work through that umbrella, and important that we absolutely continue to have that dialogue."
Ms Cooper said: "That's not an answer. Do you have any assessment of how long it will take other countries to ratify any treaty?"
And added: "Given how important the database access is, cooperation on things like people trafficking is, aren't you starting to get really worried that you just don't have a timetable to get this stuff sorted?"
Ms Patel replied: "Well I think the important point to make is that this is ongoing. This isn't just about timetabling events. And the fact of the matter is that if the House of Commons could move forward, start with the committee stage of the Bill, start landing the deal that the Prime Minister has secured, it would then move us on into the next phase of the negotiations that will take place."
She said there has been "a lot of work" in terms of engagement with the Commission.
Ms Patel was asked what level of confidence she has that a security treaty or future partnership can be negotiated and ratified by December 2020.
She said: "I think the important thing to recognise is that when you look at the way in which the Prime Minister's new deal has come together in not just a short period of time but with very significant changes, that's through engagement.”
Ms Patel said they are "conscious of time frames" but said dialogue is "ongoing".
Ms Cooper told Ms Patel: "If you able to write to us with any form of timeline or assessment that would be immensely helpful and reassuring because otherwise your answers are quite worrying."
Ms Patel appearance in front of the committee was questioned on Tuesday when Ms Cooper raised a point of order in the Commons. She said: “The Home Affairs Committee was due to take evidence from the Home Secretary tomorrow [Wednesday] afternoon. I have been trying to speak to the Home Secretary today, because she has now informed the Committee that she does not want to give evidence tomorrow.”
But when Ms Cooper said they had offered revised timings Ms Patel nodded to indicate she would attend.
Ms Cooper added: “I can see the Home Secretary nodding; I hope she can now agree to give evidence tomorrow morning, because we have been seeking to get this session in the diary since the beginning of August.”