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Former UK regulator Sir Alasdair Breckenridge said new cancer drugs could be among those affected.
Health Secretary Jeremy Hunt said he did not expect the UK to remain within the European Medicines Agency (EMA).
The Department for Health said Brexit offered new opportunities to bring timely access to new drugs.
Sir Alasdair told
BBC Radio 4's Today programme
: "The UK market compared to the European market of course is small and they may decide not to come to the United Kingdom.
"So therefore there will be delay in getting new drugs - important new drugs, anti-cancer drugs, anti-infective drugs - for patients in the UK."
The EMA authorises drugs for use across the EU and is currently based in the UK, although it is expected to leave after Brexit.
Sir Alasdair - who was the chairman of the UK's Medicines and Healthcare products Regulatory Agency (MHRA) for almost a decade - said companies could be slower to seek permission for Britain alone, as they may need to pay for a separate assessment of their product for use in the country.
His concerns echo those expressed by the current MHRA chairman Professor Sir Michael Rawlins, who said the UK could be at the back of the queue behind Japan, the US and the EU when drugs are introduced.
In previously unreported comments in January, he told peers: "One of the biggest worries I have about Brexit and standing alone as a regulator is that we are only 3% of the world market for new drugs and if we are not careful we are going to be at the back of the queue."
The UK needed to carry out regulation more efficiently to cope, he added.
'Two-year delays'
In January Jeremy Hunt said he did not expect the UK to remain within the EMA but was "hopeful" of being able to continue working closely with the regulator.
"Separate regulatory arrangements" would be put in place, he added.
David Jeffreys, the vice-president of Eisai - a Japanese drugs firm that employs 450 people in the UK - said British patients could face delays of up to two years.
He said: "The early innovative medicines will be applied for in the USA, in Japan and through the European system and the UK will be in the second or indeed the third wave so UK patients may be getting medicines, 12, 18, 24 months later than they would if we remained in the European system."
Mr Jeffreys, who also speaks for the trade body the Association of the British Pharmaceutical Industry (ABPI), said they wanted the UK to agree a co-operation deal with the EMA, even if it did not remain part of the EU system.
The former chief executive of the MHRA, Sir Kent Woods, said he believed an agreement could be reached between the UK and the EU for drug regulation in the future, but was concerned about the issue getting absorbed in a wider debate about trade terms.
Moving the EMA from London could put its work overseeing the safety of medicines imported from outside the EU at risk, he added.
'Faster access'
The Department of Health said ensuring patients have timely access to safe and effective medicines remains a priority for the government.
A spokeswoman added: "In fact, Brexit brings opportunities in this area, and we will be focused on whether we can secure even faster access to the latest innovations for British patients.
"So we are already taking action to ensure the UK continues to be a world leader and our cross-agency Brexit taskforce is considering the future regulatory roles the MHRA could adopt."
The EMA is subject to rulings by the European Court of Justice, and Prime Minister Theresa May has said the UK must be outside the court's jurisdiction.
(BBC)
