This article is the subject of a legal complaint made on behalf of Lynton Crosby.

The lobbying firm founded by the Tories' chief election strategist, Lynton Crosby, advised private healthcare providers on how to exploit perceived "failings" in the NHS, according to a leaked document obtained by the Guardian.

The existence of the presentation by Crosby Textor to the H5 Private Healthcare Alliance will add to pressure on David Cameron, who on Sunday declined once again to say whether he discussed tobacco policy with Crosby, whose company advises Philip Morris International.

Labour warned of a "shocking conflict of interest" involving the man charged with running the Tory general election campaign.

The leaked document – which consists of slides from a presentation – show that Crosby Textor advised the H5 Private Healthcare Alliance on how to promote themselves amid a highly sensitive debate on the future of the NHS.

The slides state that people believe the NHS provides good healthcare, though they believe it has "failings" and is "too bureaucratic with long waiting lists". Crosby Textor advised its clients that 63% of those questioned in a poll conducted for the presentation believed that "going private frees up the NHS waiting list".

The H5 Private Healthcare Alliance advised by Crosby Textor was an umbrella group for private healthcare providers established in December 2010 before the publication of the government's highly controversial health and social care bill. The bill devolved commissioning powers to GPs and relaxed the rules for private providers, though the initial plans were tightened under pressure from the Liberal Democrats.

Crosby Textor, which conducts polls on behalf of clients to help them develop a "powerful strategy focused on the most persuadable 'swing' targets", found overwhelming support for private healthcare providers in a survey carried out for the H5 Alliance.

It found that 59% of those polled agreed with the proposition: "In the end, it does not matter if we have a taxpayer-funded health system or a private healthcare system, as long as people get the best available healthcare."

The presentation then included quotes about the NHS, believed to be some of the 1,007 people polled on behalf of Crosby Textor. One person said: "We need to try something new because the current system isn't working." Another said: "I think the present system is exhausted."

In the presentation, Crosby Textor advised its private healthcare clients that members of the public take a pragmatic approach to the provision of healthcare. It said: "The public have no ideological objection to private healthcare and don't object to people using it if they can afford it. Private healthcare is an aspiration for the majority of people. They are put off by perceived high costs, not dogma. The British people are proud of the NHS, but also supportive of a role for private hospitals in Britain's overall healthcare system."

The presentation was made by Crosby Textor, known as CTF Partners in Britain, towards the end of 2010. This was months before the health and social care bill was given its second reading in the House of Commons in January 2011.

The publication of the bill was delayed from late 2010 – the time of the Crosby Textor presentation – amid concerns in Downing Street that the then health secretary, Andrew Lansley, had failed to think through his plans to devolve commissioning powers to GPs. The Liberal Democrats later forced a lengthy "pause" in the bill amid fears that it would boost the role of private providers.

Andy Burnham, the shadow health secretary, said of the leaked documents: "The more we learn of Lynton Crosby's business dealings, the greater the number of question marks left hanging over the conduct and integrity of David Cameron's government. It simply cannot be right to have people paid to lobby for private health organisations wandering round Downing Street when policies are being discussed that could benefit their clients. It is more evidence of a shocking conflict of interest that David Cameron has created at the heart of his government."

Burnham added that soon after Crosby started to work again for the Conservatives in November last year, the government appeared to try to reverse some of the changes to its health reforms. Labour depicted these at the time as a backdoor privatisation of the NHS after the regulations, published in February this year, said: "An arrangement for the provision of healthcare services for the purposes of the NHS must not include any restrictions on competition that are not necessary for the attainment of intended outcomes which are beneficial for people who use such services." They were later watered down. The shadow health secretary added : "Shortly after Lynton Crosby started work for the Conservative party, the government shifted its position in favour of private health companies by trying to sneak NHS regulations through the house forcing services out to the market. At the time, experts expressed surprise at the sudden shift in position. Now we can guess why. Once again, it is more proof that you can't trust David Cameron with the NHS."

A Crosby Textor source said the work was carried out before Crosby started to work again for the Conservative leadership. The source said it would be inappropriate to comment because the research was commissioned by a client.

A Conservative spokesman said in response to the leaked documents: "The prime minister has been clear that Lynton Crosby has never lobbied him on anything. Lynton Crosby is an adviser to the Conservative party. He does not advise on government policy."

The new revelations about Crosby's business interests came as the prime minister declined once again to say whether he discussed the government's plans to abandon plain packaging for cigarettes with Crosby, whose company advised Philip Morris International. Cameron told the Andrew Marr Show on BBC1: "I think there's been a bit of a red herring running last week … Let me be clear: he has not intervened in any way on this or indeed on other issues."