Some 61 per cent of those aged over 65 say they are worried about the impact of Brexit, a 34 percentage point increase since September 2016, when Which? began recording the data.
Among those aged 18 to 34, 64 per cent say they are concerned about the consequences of Brexit, the consumer group said.
But Which? also found a rise among the 34 to 64 age group who say they are concerned since September 2016, an increase of 24 percentage points to the current 60 per cent.
The poll was published as Theresa May came under intense pressure to publish the legal advice behind her Brexit plan as Labour, Tory Eurosceptics and the Democratic Unionist Party line up against her.
Brexiteers, including Environment Secretary Michael Gove, want to see the full legal advice setting out how any customs arrangement to avoid a hard Irish border could be ended to avoid it becoming a permanent settlement.
The DUP, whose 10 MPs prop up the Prime Minister’s administration in the Commons, said it was “in the public interest” for the legal advice to be disclosed.
For Labour, shadow Brexit secretary Sir Keir Starmer said it was “essential” that MPs should be able to see the advice drawn up by Attorney General Geoffrey Cox.
Liberal Democrat Brexit spokesman Tom Brake said refusal to publish the advice “raises serious questions about what Tory ministers are trying to hide”.
In a development that will cause concern in Downing Street, a Tory European Research Group source indicated its MPs “would be up for sharing the Attorney General’s wisdom” if Labour forced a Commons vote.
Pressure over the legal advice mounted as Cabinet ministers were invited to review the text of the withdrawal agreement which has so far been secured in negotiations with Brussels.
The Prime Minister told MPs last month that 95 per cent of the deal had been agreed, although the key sticking point of the backstop to prevent a hard border between Ireland and Northern Ireland remained unresolved.
Overall, 62 per cent of people in the UK say they are worried about the impact of Brexit, up from 39 per cent in 2016.
Concern is currently at 65 per cent in Scotland, 63 per cent in Northern Ireland and 61 per cent in England, the watchdog found.
Which? director of policy Caroline Normand said: “The continuing lack of certainty about how the UK will leave the EU is clearly concerning people as they consider what it could mean for families and businesses across Britain.
“Consumers want a Brexit that protects and enhances their rights and gives them access to a wider range of high-quality, affordable goods and services.”