The data from NatCen Social Research – based on the views of some 3,300 people – also shows a widespread anxiety about the prospect of further spending cuts.
But for the first time in nearly a decade, there was a rise in the number of those who think spending and taxes should be increased, the report says.
It comes after news the UK economy shrank by less than thought up to June.
The latest revised data from the Office for National Statistics found the economy contracted by 0.5% during the quarter between April and June – less than the 0.7% it announced in July.
The British Social Attitudes survey asks more than 3,000 people every year what it is like to live in Britain and how they think Britain is run.
Despite the tough economic climate, the study by independent social research agency NatCen reveals attitudes towards welfare and welfare claimants have toughened.
Only 28% of those asked wanted to see more spending on welfare – down from 35% at the beginning of the recession in 2008, and from 58% in 1991.
Report author and NatCen chief executive, Penny Young, said the study showed the public’s view on welfare was “in tune… with the coalition’s policies”.
She said: “The recession doesn’t seem to be changing things; attitudes continue to harden.
“One thing that we’ve seen is that even where groups are seen as perhaps more deserving – so retired people, disabled people – again for the first time since 2008 we’ve seen that the number of people who are prepared to see more money go on disability benefits has actually fallen.”
And on immigration, the report suggests British people “strongly favour migrants they see to be socially beneficial”, according to the report.
Some 51% would like to see immigration levels “reduce a lot”, a figure which has risen from 39% in 1995.
The data also shows a further 24% would like to see levels “reduce a little”.
Meanwhile, the proportion of people who want to see further public spending – even if this requires higher taxes – jumped from 31% to 36% between 2010 and 2011, after falling for nearly a decade from 63% in 2002.
More than half – 55% – would like spending levels to stay where they are.
At the same time, the report reveals many Britons are worried about the impact of spending cuts on public services, particularly education and health.
Satisfaction with the NHS fell from 70% in 2010 to 58% in 2011, according to the figures.