A government review looking into freedom of movement across the EU has not recommended any sweeping reforms to immigration rules in a report likely to disappoint Conservative Eurosceptics.

The Whitehall report found the effects of free movement on the labour market are largely viewed as positive, although it acknowledged there is less consensus about the benefits of low-skilled migration than high-skilled migration.

The review was published after being delayed because there was unhappiness within the Conservatives that it did not appear to be tough enough on immigration. After a rewrite, the Liberal Democrats in the coalition protested that it was then too critical of the EU rules, with the business secretary, Vince Cable, accusing his coalition partners of taking a "propagandist" approach.

The resulting compromise report does not come down on any side of the debate, except to raise the prospect of a review of benefits for migrants to "ensure they are fit for purpose" – a policy already announced by David Cameron. The report warned that public support for free movement could be undermined if the issue of EU migrants being able to claim benefits is not addressed.

It found some pressure on primary school places and housing similar to the effect of immigration from other countries but "little hard evidence regarding problems with community cohesion". It also noted a need to address concerns about criminality and abuse of freedom of movement rights by a small minority of EU immigrants.

But it fails to provide any evidence as ammunition for Conservative backbenchers pushing Cameron and Philip Hammond, the new foreign secretary, to secure radical reforms of free movement with the agreement of other EU member states.

The report was one of 11 "balance of competence" reviews published on Tuesday, the last day before MPs break up for the summer. Matthew Elliott, chief executive of Business for Britain, a lobby group seeking reform of the EU, said it was "a missed opportunity, because it fails to suggest the substantial reforms Britain should seek or, worse still, implies that the status quo is broadly appropriate".

"Both the public and business leaders want significant changes, not more of the same," he said.

The report does, however, raise some of the options that Cameron could consider when trying to negotiate reforms. These include a suggestion by David Goodhart, of the Demos thinktank, that free movement could be scaled back to a system that gave preference to "national citizens" in the labour market.

Another idea is that new countries should not be allowed access to free movement rights until their national income is 75% of the EU average, reducing the possibility of mass migrations of people from poorer nations that has previously been criticised by Cameron. Both these would require treaty change and the agree of all member states, the report warns.