The Government has guaranteed "full plans" are in place to deliver an unhindered supply of medicines in the event of a no-deal Brexit.
Health Secretary Matt Hancock also said a £1.8 billion boost for the NHS has nothing to do with preparing for a possible general election.
Speaking to ITV's Good Morning Britain, Mr Hancock said: "I guarantee that we now have all plans in place to make sure that the NHS will be prepared whatever the Brexit scenario."
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He added: "There are 12,000 medicines that are generally prescribed, licensed to be prescribed in Britain, and in normal times there are always a handful which are in short supply and we are constantly, in fact we have a unit within the department which constantly works on these to make sure there is always that unhindered flow and the plans we have got are for that to continue exactly as normal through a no-deal Brexit if that is what is necessary."
Mr Hancock said: "The thing is, in the health service, one of the things I have learned as Health Secretary is that this is a risk-based business. Keeping people alive is very hard work. This is what hospitals do all the time.
"What I can guarantee to you is that we have full plans in place to deliver the unhindered supply of medicines and to make sure the NHS runs as effectively as it does today through any Brexit scenario."
Speaking on BBC News, Mr Hancock said the money to pay for a £1.8 billion cash injection for the NHS is "tax payers' money".
He said: "The economy is growing strongly and, ultimately, all public services, the long list you gave, and of course the biggest amongst them is the NHS, they are paid for by having a strong economy.
"There is a record number of people in work at the moment, that means a record number of people paying income tax, a record low number of people who are claiming unemployment, so that gives you more money."
He added: "That money is now, and that money for the NHS is flowing in this year, it is immediate. We've got the 20 upgrades where the shovels can go in the ground."
Shadow health secretary Jon Ashworth, however, said there is "scepticism" about whether the cash boost is new money.
Speaking on BBC Radio 4's Today Programme, Mr Ashworth said: "What it is beginning to look like is that money hospitals were promised for cutting their costs and cutting back on their spending, they were promised extra money and then ministers came along and blocked them from spending this extra money.
"It now looks like all Boris Johnson has actually done is said they can spend that extra money after all. So there is huge scepticism about whether it is new money."
Mr Hancock added: "Only 10 days ago Boris Johnson became Prime Minister, he stood on the steps of Downing Street and he said that we were going to upgrade 20 hospitals, and 10 days later here we are making the commitment."
Asked whether the £1.8 billion boost is part of a bid to "sweeten up" the public in a run up to a possible general election, Mr Hancock said this is not the case.
Mr Hancock told Good Morning Britain: "I'm concentrating on delivering for the NHS. That isn't a discussion I've had with anybody other than the people who keep asking me about it in the media.
"This money is because the NHS is our number one domestic priority. People rely on it every day and we are absolutely determined to make sure the NHS is the best it possibly can be."