With the London Olympics a month away, both the Tories and Labour are trying to turn the Games to their advantage

A discreet political battle about the Olympics is expected to start next week when David Cameron makes his first speech on the Games, trying to set the events in a patriotic context, while Labour starts to suggest that they might not have happened at all but for an interventionist "big" government approach.

The political parties have tried to keep the month of sports as a cross-party national celebration, in recognition that the public will want politics to take a back seat. But senior ministers will be having a series of political and trade bilaterals throughout the Games as visiting politicians, including US Republican presidential candidate Mitt Romney and Russian president Vladimir Putin, arrive.

One Downing Street source said: "The diaries are just starting to fill with nothing but the Olympics."

There are also nerves that if things go wrong, such as with the opening ceremony, transport, immigration queues at Heathrow, or ticketing, the event could backfire and the government's reputation for competence – already under question after U-turns following the budget – will be further dented.

The culture secretary, Jeremy Hunt, has described the Games as a business opportunity for Britain, saying: "There will never be another opportunity like this in our history. It isn't just about the ceremonies, it's about how competently we put on the biggest sporting event on the planet. I see it as a great business opportunity – businesses are choosing where to invest, students where to study … If you get the Olympic opening ceremony right, you strengthen your national brand. This is a once-in-a-lifetime opportunity."

Hunt, keeping a low public profile since his inquisition at the Leveson inquiry, has even been jumpy about any subliminal or overt messages in the opening ceremony. Hunt's aides were concerned about the deployment of hundreds of NHS staff in the opening ceremony by Danny Boyle, the film director, fearing it could be taken as a sly dig at the government over its controversial health reforms. Hunt was initially nervous about their inclusion, but was told that Cameron had no objections.

Labour, which is holding a fundraising event built around sport in a fortnight at the Emirates stadium in London hosted by Tony Blair, is putting its own interpretation on the political value of the Games. Blair was instrumental in winning the games.

In a recent article for the Labour pressure group Progress, Tessa Jowell, the former culture secretary, who oversaw the bid for the Games for London in 2005, argued it was vital to learn from the experience of the Games about the value of public-private partnerships, including how they can support key industries.

She wrote: "There are clear lessons that can be drawn for government when taking on projects of this nature. That the government needs to support the project wholeheartedly and seek to fashion a cross-party consensus. That the right level of funding needs to be secured from the Treasury, but that it then very quickly needs to get out of the way. That the scope and nature of the project, its timescale and the level of available funding needs to be clearly defined by government – and then they need to hire the best people in the world to achieve it."

She argued: "The focus on regeneration and local benefit not only built better relationships with local residents but also created a supportive culture within the workforce that 'failure was not an option' and that everything had to be done to make the project a success."

She added: "The construction work also showed the employer and trade unions need to be engaged in co-operation rather than confrontation."

Some Labour officials are hoping to draw Blair towards closer explicit support for Labour in the next few months and believe the Olympics could help.

They are hoping he will argue that the Olympics show the limits of a totally free market, and the continuing role of the state.