Most Britons believe trade unions are essential to protect workers' interests, although some have concerns about their links to the Labour Party.
The findings come amid the London tube strike, which has seen members of the Rail, Maritime and Transport Workers Union (RMT) and the Transport Salaried Staffs' Association walk-out over job losses.
According to researcher Ipsos MORI, more than three in four (77%) Britons agree that trade unions are essential to protect workers' interests while only 14% disagree.
Labour supporters (84%) and workers in the public sector (90%) are particularly likely to see trade unions as essential, compared to 65% of Conservatives.
The importance of trade unions to the public has remained fairly constant ever since 1975 when Ipsos MORI first began asking the question.
In 1975, for example, 73% believed trade unions to be essential, peaking at 82% in 1994.
"For the last ten years trade unions/strikes have not been mentioned by more than 1% of Britons in the Ipsos MORI Issues Index, while in the late 1970s it was once seen as the number one most important issue," said Gideon Skinner, head of political research at Ipsos MORI.
"This is reflected in the current public mood – trade unions are seen as vital for the workers they represent, and there is much less concern about them wielding too much power than in the past."
The researcher said one perception of trade unions that has changed considerably over that time is the belief that trade unions have too much power in Britain today.
Three in ten (29%) British adults now believe trade unions to be too powerful including 46% of Conservatives (and only 23% of Labour supporters).
That is significantly lower than in the 1970s and early 1980s when up to eight in ten felt they had too much power (80% in September 1979), but it is slightly higher than the mid-1990s when around a quarter said the same (24% in August 1995).
Around four in ten (42%) Britons agree that trade unions would have too much power under a Labour government.
This is higher than was the belief when Labour was last in opposition in 1994 and 1995 when 37% and 34% agreed respectively, though in 1992 around half of Britons were concerned that Labour would have too much power under a Labour government.
The researcher said just 15% believe trade unions would have too much power under a Conservative government.