Lady Hermon has said a no-deal Brexit would be an enormous threat to the stability of the UK.
She told BBC Radio Ulster's Inside Politics programme "we absolutely must prevent there being a no-deal Brexit and a hard border on the island of Ireland".
The Independent Unionist MP said this was because of its political and security implications.
Lady Hermon is the only non-DUP MP from NI who takes her seat in the Commons.
The North Down MP voted in favour of the prime minister's EU Withdrawal Agreement.
She said Theresa May "doesn't have the option to bin the Irish border backstop" as "it's in the deal and it is there to protect the peace we have enjoyed for the past 20 years".
Asked if the prime minister could lose her support if she bent too far in the direction of the DUP, Lady Hermon said that was something she would "have to think long and hard about".
As a former remainer, Lady Hermon said she felt she has compromised in backing the government's deal.
She argued that it is now up to the DUP and the Conservative Brexiteers who oppose the backstop "to show how pragmatic they are".
Lady Hermon said she did not think extending Article 50, the process by which the UK is due to exit the EU, is a good idea.
She said holding another round of European parliamentary elections would be a nonsense.
Lady Hermon said she also opposed holding another EU referendum, describing it as a "false hope" and a "non starter".
She said she believed another referendum does not have sufficient backing amongst MPs and could not be arranged in the time available.
Lady Hermon said she believed how MPs would vote on the range of amendments to be put before the Commons next Tuesday remains "anybody's guess".
She added that she thinks neither the DUP nor the Brexiteers of the European Research Group will know until Tuesday night whether they "may have overplayed their hand".
Lady Hermon described the Queen's comments urging the people of the UK to find "common ground" as very timely and absolutely appropriate.
She said the atmosphere in the House of Commons was "grim", adding that "it's also grim throughout the country, and particularly in Northern Ireland".
She expressed dismay that there is now "this tension, this real difficulty, where we have had this very close working relationship with the Republic of Ireland".
Lady Hermon referenced the Good Friday Agreement of 1998 and highlighted "20 years of peace in my lifetime which has been wonderful".
She said she had friends who "self identify as Irish nationalists" and who are heartbroken about the way the UK and the Republic of Ireland are moving in different directions.
"I am heartbroken for them that we are now in this difficult situation," she added.
"So the Queen's words have to be listened to, we have to find a centre ground that can deliver Brexit with the least friction and stress and upset for everybody on these islands, whether nationalist, republican, unionist or other."