David Cameron must find more allies across Europe if he is to secure meaningful change to freedom of movement rules, a pro-EU think tank said.
An analysis of the UK's clout in Brussels - compiled by a panel including senior politicians - found it was far stronger than voters believed, blaming a British "victim syndrome".
But the British Influence report suggested the Prime Minister's stated desire to curb immigration from new member states so far lacked sufficient backers in other capitals.
Mr Cameron has floated the idea of preventing workers from accession states moving elsewhere in the EU until their own economies were performing at a certain level.
The end of restrictions on Bulgarian and Romanian citizens on January 1 has fuelled pressure from Tory MPs concerned about the electoral threat of Ukip for action on immigration.
The report - whose contributors included former foreign secretary Sir Malcolm Rifkind and ex-Liberal Democrat leader Sir Menzies Campbell - noted that countries such as Germany and the Netherlands shared concerns about so-called benefit tourism.
But it added: "The UK will need support from a wider group of member states, including some in central and eastern Europe, if it is to alter the rules in significant ways".
A number of high-profile eastern European figures - including Polish prime minister Donald Tusk and Hungarian EU commissioner Laszlo Andor - have strongly criticised Mr Cameron's tough stance.
The report for British Influence suggested Britain was on track to achieve 90% of policy goals - despite polls showing most people thought the country was a "loser".
Countering that gap was crucial to securing a vote in favour of continued membership in any future in/out referendum, it said, calling for stronger leadership from the Government.
Mr Cameron has pledged to negotiate better terms of membership to put to voters in an in/out referendum by 2017 if the Conservatives hold power after the 2015 general election.
Three in five (60%) of those canvassed by YouGov for the group said the UK enjoyed little or no influence with almost two-thirds (65%) believing France and Germany call the shots.
A similar proportion (62%) believed British aims were "mostly or always rejected".
Demonstrating that London enjoyed the backing of allies within the EU, though, would be enough to dramatically increase support for staying in - with 50% then opposing exit, it found.
British Influence director Peter Wilding said: "This perception gap is due to some sort of 'victim syndrome' with our EU membership.
"In focus groups, voters told us that Britain was 'insignificant' and 'losing against the Germans and French'.
"In fact the scorecard shows that Britain has more impact on key EU decisions than the public perceives and is on track to achieve 90% of its policy goals. Voters are crying out for stronger leadership from Britain in Europe."
The group's "scorecard" examined a range of policy areas.
It found the UK was successful in 18, did well in 20 more and failed in only four - including on the proposed Financial Transactions Tax against which the UK has made a legal challenge.
Sir Malcolm said the UK government and parliament needed to demonstrate a tough stance by better using existing powers - known as the "yellow card" - to join with other member states to object to unwelcome EU proposals.
Eurosceptics are calling for a national veto to be introduced but the senior Tory warned against "unrealistic and unworkable ruses".
"It is by playing the system more cleverly from the inside, rather than being tempted towards unrealistic and unworkable ruses that foster disappointment and disillusion, that we can deliver what we most desire - a powerful Britain within a reformed European Union," he said.
The Netherlands Ambassador to the UK Laetitia van den Assum joined the politicians in the panel calling for a less hostile approach to the negotiations.
Britain had "always been a critical force for change within the EU", she said.
"It should lead probably much more as one of 28, who wants to use arguments and facts in order to bring others around to its points of view.
"It should not try to dictate that unless it gets what it thinks it needs, it will leave."