Speaking during a public phone-in while appearing on a LBC radio show, the prime minister was asked if the government was making provisions about the access to medicine in the event of the UK leaving the EU without a deal.
Ms May responded by saying that this was an issue that affected her personally and that the Department of Health was taking steps to ensure there were ample supplies.
She said the insulin she used to treat her type one diabetes was manufactured in Denmark.
“This is an issue that affects me personally. I am a type one diabetic, I depended on insulin every day. As it happens my insulin is produced by a company in the EU,” Ms May said.
“…I know that this is an issue that is a matter of importance to people and that the Department of Health is ensuring that it is taking all the steps.”
Ms May faced questions from members of public about her Brexit deal, her future as prime minister and the ministerial resignations that have taken place over the last week.
When quizzed on the infamous Brexit claim that the NHS would receive an additional £350 million a week, she referred to announcements from Phillip Hammond’s budget last month
“When we leave the EU we won’t be sending the vast amounts of money to the EU every year that we do at the moment,” Ms May said on LBC.
“…That means we will have money to spend on priorities like the NHS. This is our number one spending priority and we have already committed to spending more money on the NHS over the next five years.
“It will mean £394 million more a week going into the NHS.”
However, the PM repeatedly refused to condemn former foreign secretary Boris Johnson for campaigning for Brexit in front of the bus that bore the £350m claim.
The prime minister was also subjected to repeated calls to stand down, to make way for Brexit-supporting politicians, told the Conservative Party’s coalition partners the DUP would withdraw support unless there was a change of leader, and she was compared to former prime minister Neville Chamberlain, who attempted to make peace with Nazi Germany ahead of the Second World War.
In the lengthy appearance, Ms May defended her plan, admitted there had been compromises, but maintained her belief the plan was the best deal for the UK.
One Conservative-supporting councillor Dan, from Louth, said Ms May should stand down, saying he "commended" the PM for trying to strike a Brexit deal with the EU, but "sadly that has not worked".
He said: “Please Prime Minister, tell me why do you think you should stay on as PM when you have failed - despite your no doubt honourable intentions - to (deliver on) the referendum result?
"If you cannot do that, I respectfully ask you to do the right thing in the national interest and stand down to allow someone from the Brexit camp to take the lead. There is still time to sort this out."
Ms May responded by going through details of the draft withdrawal agreement.
She said: “You're absolutely right that for a lot of people who voted Leave, what they wanted to do was make sure that decisions on things like who can come into this country would be taken by us here in the UK, and not by Brussels, and that's exactly what the deal I've negotiated delivers.”
During her half-hour appearance on the show, host Nick Ferrari also told the prime minister DUP leader Arlene Foster had said the party was “ready to withdraw support unless there was a change of prime minister”.
“They’ve raised some questions with us, they’ve raised some concerns with us”, Ms May conceded, and added she believed she still had the DUP’s support for the Brexit deal.
Agencies contributed to this report
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