The UK has been warned by the pharmaceutical industry that some stockpiles of medical supplies have been "used up entirely" by the virus.
A memo seen by the BBC advises the government to buy and store "critical" medicines to treat the virus.
Drug makers fear stockpiles cannot feasibly be built back up again in time, if the UK should fail to strike a post-Brexit trade deal with the EU.
The government said "robust contingency plans are in place".
The spokesperson added: "We want a relationship with the EU which is based on friendly cooperation between sovereign equals and centred on free trade."
However, firms fear disruption to global supply chains will seriously impact the NHS.
The internal pharmaceutical industry memo, which was prepared for the government in May, warns that after the pandemic ends, there will be "less or zero product available in the market to allow for stockpiling a broad range of products" than there was in 2019, when stockpiling occurred in preparation for a possible no-deal Brexit.
At the time, the industry itself paid for six weeks' worth of stockpiles.
"Preparations for the end of the transition period must complement plans to secure the supply of coronavirus therapeutic and supportive products," the memo says.
The pandemic has led to a massive increase in demand for medicines not previously stockpiled for critical care and respiratory medicines, such as inhalers.
At the same time, coronavirus lockdown measures imposed by governments have caused significant supply bottlenecks due to factory closures and export bans, as well as a drastic decline in air freight.
The memo was put together by a cross section of pharmaceutical industry groups anticipating preparations for a failure to strike a trade deal with the EU, alongside a refusal to extend the negotiating period.
If this happens, the UK would trade on World Trade Organization (WTO) terms, which would mean trade barriers from the start of next year.
Keeping the flow of medicines going
The memo goes on to remind the government that the flow of medicines has been kept going through the pandemic thanks to "international coordination and information sharing within global companies to ramp up, and where necessary, redirect manufacturing".
As a result, the pharmaceutical industry writes: "We would warn against any drastic policies mandating wholesale changes to global supply chains, as this could fundamentally disrupt the supply of medicines for the NHS and patients in other countries."
The pharmaceutical industry has long anticipated that a no-deal Brexit could cause congestion at the ports of Dover and Calais, which is the route that 90% of imported drugs and medicines from the EU take to get to the UK.
As a result, the industry has advised that the government itself will have to buy and store a longer list of "critical products" where "supply could be challenging due to either COVID-19 or the end of the [Brexit] transition period".
The need for trading stability is even more important this year, because the pattern of demand for medicines is likely to be very different to normal.
That means, the memo says, that the government needs to develop a new broader list of critical products which "reflect the challenges posed by both the end of the transition period and continues response" to the coronavirus crisis.
Urgent government action needed
The memo also emphasises that the government needs to be storing a much broader list of medicines going forward, because of the joint challenge of the pandemic and in the event of a no-deal Brexit deal at the end of this year.
But the pharmaceutical industry says that to have significant impact, the stockpiling will have to start in the next few weeks, and even after the pandemic ends, stockpiling will not be possible for every medicine required.
In a normal year, Christmas would be "the worst time of year to ask companies to increase their stockpile levels", the memo says.
The pharmaceutical industry is expecting the system of no-deal government-chartered freight ferries and aeroplanes to be re-established, given that border disruption is expected at the end of the Brexit transition period. It says the government needs to signal that this will be the case by next month.
And it has requested "urgent clarity" on the implementation of arrangements for Irish Sea trade, under the Northern Ireland Protocol.
The Association of the British Pharmaceutical Industry (ABPI), one of the organisations involved in drafting the report, says firms had "worked around the clock" during the pandemic to make sure medicine supply chains held up.
"With this pressure likely to continue over the coming months, the pandemic has reinforced why it is essential that the UK and EU reach a deal on their future relationship," said ABPI's chief executive Dr Richard Torbett.
In the meantime, he said its members would continue to work closely with government to put detailed plans in place.
"But not everything is in the gift of industry. Stockpiling is one element - having alternative supply routes and making sure that goods can continue to flow uninterrupted across borders is also critical," he stressed.