The WSTA survey revealed that 64% thought the current level of tax on spirits was too high, and 57% thought the same about the tax on wine.
On average, 74% or £7.26 spent on a 70cl bottle of spirits goes to the Treasury, as does 55% or £2.05 for a bottle of wine.
Most respondents were unaware that Britain had some of the highest duty rates in the EU, however.
Only 12% knew the current level of tax on spirits, while just 16% were properly informed about the tax on wine.
Miles Beale, chief executive of the WSTA, said: “This YouGov poll shows that the majority of people are in the dark about how much the taxman is taking from them when they buy a bottle of wine or spirits.
“When they are put in the picture there is a dramatic leap in the number of people who think British consumer are being hit for too much tax.
“And it’s not hard to see why. Wine is the nation’s most popular drink, yet wine duty is the second highest in the EU and UK spirits duty is the fourth highest.
“The industry is asking for a 2% cut in the March Budget to build on what the Chancellor started last year, and to create jobs, encourage investment and grow exports.”
Jonathan Isaby, chief executive of the TaxPayers’ Alliance, which is supporting the industry-wide campaign for a tax cut, said: "This polling reveals just how strongly taxpayers feel politicians are adding to their cost of living. British consumers are being treated incredibly unfairly with too-high taxes on everyday goods which hit the poorest hardest.
“Politicians often talk the talk, but if they are sincere about helping hard-pressed families with their bills then cutting this regressive tax would be a good place to start."
Another poll published this week by the BBPA revealed that 72% of voters back a cut or freeze in beer duty.
Only 20% think the current level of tax on beer is fair, the poll showed.
UK beer duty rates are three times higher than the EU average, and a whopping 13 times higher than in Germany, the EU’s largest beer market.
Brigid Simmonds, chief executive of the BBPA, said: “This new poll shows the public understands how important pubs are to local people, and how a penny off a pint is the simplest and best way to give pubs a boost.
“George Osborne has been in tune with the public so far, with his three beer tax cuts saving pubgoers millions. He can keep up the good work, with another penny off a pint in the Budget.”