The Prime Minister avoided putting an amount the Government was prepared to pay the EU to leave as she added that “no deal is better than a bad deal”.
But Mrs May did not elaborate to Mr Paxman about on what she considered a "bad deal" to be.
She said: "It isn't a question of what it's worth paying to get out, it's a question of what is going to be the right deal for us to leave the European Union, which will stop us from paying huge sums of money into the EU every single year, which will enable us to have control of our money, of our borders and our laws."
Jeremy Paxman pushed Theresa May on how much she will be willing to pay to leave the EU
What I'll be doing is being a difficult woman and ensuring we're negotiating hard
When asked whether she was prepared to walk away without a Brexit deal, Mrs May replied: "I think you have to. In negotiations you have to recognise that you're not in there to get a deal at any price.
"We're in there to get the best deal for the United Kingdom, and actually I'm optimistic about that because I think in the European Union they want to continue their relationship with us as well."
She added: "What I'll be doing is being a difficult woman and ensuring we're negotiating hard."
Brexit Negotiations: Britain's sternest enemies Tue, April 4, 2017
According to a new index, the EU27 countries fall into three groups: hard-core, hard and soft. These are the countries with the highest scores which indicate a fairly strong opposition to Britain’s position
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France has the highest score in the index at 32.5
Mrs May was also repeatedly pressed by the TV interviewer about whether she had changed her mind on Brexit after she supported Remain during last year's referendum campaign.
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The Tory leader replied: "I also said that the sky wouldn't fall in if we left the European Union."
"I believe that we are doing the right thing in making a success of Brexit."