* Cameron is making second Indian visit as PM
* Hopes India may consider Eurofighter if French deal fails
* EU states clamouring to boost trade relations with India
* Bribery scandal engulfs Anglo-Italian helicopter deal
British Prime Minister David Cameron arrived in India on Monday as a graft scandal engulfed an Anglo-Italian helicopter deal and immediately told his hosts they should open up their economy because Britain has done the same for Indian firms.
Making his second visit to India as prime minister, Cameron's trip comes days after a similar trade mission by French President Francois Hollande, underlining how Europe's debt-stricken states are competing to tap into one of the world's fastest-growing economies.
Cameron's delegation, which includes representatives of more than 100 companies, is the biggest taken abroad by a British prime minister and includes four ministers and nine members of parliament.
Cameron said he was proud of the fact that Indian companies like TATA group, the owner Jaguar Land Rover, had such a strong foothold in the British economy, but said he expected a reciprocal arrangement.
"Britain is an open economy and we encourage that investment," he said. "I think, in return, we should be having a conversation about opening up the Indian economy, making it easier to do business here, allowing insurance and banking companies to do more foreign direct investment."
India was still saddled with outdated rules and regulations, Cameron complained.
Investors have been clamouring for years for India to free up Asia's third-largest economy to more foreign investment. But their entreaties have been resisted by Indian opposition groups worried about potential damage to their businesses.
The timing of Cameron's trip is not ideal. India said on Friday it wanted to cancel a $750 million deal for a dozen helicopters made by AgustaWestland, the Anglo-Italian subsidiary of Italy's Finmeccanica, over bribery claims.
That will not make Cameron's job of persuading India to buy more civil and military hardware easier, and Indian officials have told the local press they intend to press Cameron for "a fully-fledged report" on what Britain knows about the scandal.
Britain has said it wants to wait until the end of the Italian investigation before commenting in full, but has given India an interim report on the subject.
At a time when Britain's government is struggling to get its economy growing, officials see India, projected to become the world's third largest economy by 2050, as a key strategic partner in what Cameron has called a "global race".
"India is going to be one of the leading nations in this century and we want to be your partner," Cameron told Indian workers at Hindustan Unilever Ltd.
During his visit, Cameron is expected to tell the Indian government that the Eurofighter jet, which is partly built in Britain, remains an attractive option if New Delhi decides to review a multi-billion dollar deal to buy 126 French-made Rafale fighters.
A British government source said on Friday that London had noted that Hollande had not finalised the Rafale fighter jet deal during his own trip and that London would be asking how the talks with the French were going.
Companies travelling with Cameron include BP, BAE Systems, De La Rue, Diageo, EADS UK, HSBC, JCB, Lloyd's, the London Stock Exchange, London Underground, Rolls-Royce and Standard Chartered.
Cameron's visit to India, which won independence from Britain in 1947 and whose colonial history remains a sensitive subject for many Indians, will take in Mumbai and New Delhi.
Cameron says the two countries enjoy a "special relationship", a term usually reserved for Britain's ties with the United States, but it is a relationship undergoing profound change. For now, Britain's economy is the sixth largest in the world and India's the 10th. But India is forecast to overtake its old colonial master in the decades ahead.
In a nod to how the relationship is evolving, Britain will stop giving India foreign aid after 2015.
Cameron is expected to lobby India to do more to allow foreign retailers such as Britain's Tesco to open stores in the country.
New Delhi changed the rules last year to allow foreign chains to operate in India but attached policy riders including obligations over local sourcing, mandatory investment in local infrastructure and restrictions on what goods could be sold.
India is forecast to spend $1 trillion in the next five years on infrastructure and Britain is hoping its firms may win some of those contracts.
Cameron said he wanted British firms to help India develop new cities and districts along a 1,000 km (600 mile) corridor between Mumbai and Bangalore, generating investment projects worth up to $25 billion.
Some British companies have run into problems in the past. Mobile phone operator Vodafone has repeatedly clashed with the Indian authorities over taxes and oil company Royal Dutch/Shell has asked the British government to raise a tax dispute it has with India during Cameron's visit.
Cameron's aim is to double bilateral trade 11.5 billion pounds in 2010, when he last visited, to 23 billion pounds in 2015. Officials say that goal remains on track.
He is expected to meet his Indian counterpart, Manmohan Singh, and to announce a clutch of deals, including cooperation agreements to help Indian cities develop metro systems.
His office said those deals would create 500 British jobs and safeguard a further 2,000.