Athletes and business leaders planning to attend the Commonwealth Games in Delhi have been privately warned to expect terrorist attacks on tourist sites and public spaces across India, the Observer has learned.

After a week in which the Games appeared to be in serious danger of cancellation, some athletes have now started to arrive in Delhi. The first representatives of England arrived on Thursday, while Scottish and Welsh competitors were due to fly in yesterday.

But a risk analysis provided to a number of national teams – believed to include some from the UK – and major corporations has highlighted the terrorist threat overshadowing the event.

The alarming assessment, by one of the world's leading security firms, helps explain why the Commonwealth Games Federation president, Michael Fennell, warned yesterday that there was still great concern about the security and safety of athletes and officials.

In a damning indictment of Delhi's ability to protect visitors, the UK-based firm Control Risks warned that the diversion of security resources to protecting the main stadiums left India without the capacity or capability to protect soft targets, with local police not up to the job.

The firm has advised its clients to stay away from tourist attractions, public places and government buildings, and not to travel by public transport.

Chietigj Bajpaee, the company's south Asia senior analyst, told the Observer that Control Risks had advised clients to expect terrorist attacks on soft targets around India in the days running up to the Games and during the Games themselves, from 3 to 14 October.

"I think there is a relatively high likelihood of attacks taking place, but these attacks may not target the Games venues themselves," he said.

"We have advised against using public transport, advised against going to certain areas, advised against going to tourist attractions in the weeks leading up to and during the event, given that security resources will be concentrated on securing the Games themselves, so other parts of the city and the country will be vulnerable.

"We have also advised that if you are a team participant you may be more vulnerable than a tourist. We have advised avoiding areas around government buildings or anything that could be considered a soft target, such as marketplaces."

The advice was vindicated when two Taiwanese tourists were shot outside the Jama Masjid, one of the largest mosques in India, in the heart of Delhi last Sunday. Initial attempts by the police to deny terrorist involvement were met with widespread disbelief and officials later pointed the finger at the Indian mujahideen, which had claimed responsibility and promised further attacks. One report, citing police sources, suggested the group had hired gunmen to attack westerners on sight.

The security warnings come at the end of a terrible week for India in which several national teams threatened to withdraw from the competition, voicing dismay at the ramshackle condition of the Games village, the collapse of a footbridge to the main stadium and the tourist shooting.

To add to visitors' concerns, the Royal Institution of Chartered Surveyors has now expressed serious misgivings about the quality of the stadiums. The institution's head in India, Sachin Sandhir, warned of serious shortcomings in the public and sporting infrastructure, despite the estimated £6.3bn spent on the Games.

"The last-minute dash to complete most venues has resulted in huge compromises on quality of projects, bypassing of clearances, and exploitation of workers," he said.

He said structures caving in or showing signs of damage so soon after being built – a ceiling within the main stadium also collapsed last week – "raise serious concerns on the structural quality, viability and safety of venues, and are indicative of the gross violations of building codes and regulations and the level of adherence to ethical professional practices".

Sandhir criticised the Games as a wasted opportunity for India to showcase its talents, blaming rampant corruption, inefficiency, a lack of trained and qualified professionals, and the allocation of construction works to ill-suited agencies. "The absolute disregard to the use of standard material and equipment has also seriously jeopardised safety of venues," he said.

In a verdict which will do little to reassure those heading for Delhi, he added: "We can now only wait and watch and be hopeful that not all the venues were subjected to this lackadaisical approach to development and, in fact, some of these will actually deliver to international standards."

Some athletes have now started to arrive in Delhi, but while organisers believe that their swift reaction to international protests – which included the prime minister, Manmohan Singh, taking personal charge – may have helped turn a corner, many parts of the city and its key Games-related projects still resemble a badly drained building site.

The first members of Team England to arrive have been staying in a five-star hotel after shocked officials deemed accommodation in the Games village unacceptable. Craig Hunter, England's chef de mission, said he was glad to see the work was being done to improve conditions in the village, but added "we are in a phase of looking at the detail, making sure that fire and safety equipment and procedures are in place and that the apartments are clean and safe. Our next wave of athletes arrives on Sunday and a lot still needs to happen before then. So more and swift action is required."

Yesterday, Fennell said there had been considerable improvements but that there was still a lot to do if the Games were to go ahead as planned. "What is of great concern is the safety and security of athletes and officials," he said.

About 7,000 athletes from 71 countries were expected to travel to Delhi, but several have pulled out, citing security fears, concerns over the accommodation and the ongoing dengue fever problem – worsened by large pools of stagnant water that have proved a breeding ground for mosquitos – as reasons enough to stay at home.

Australia's world discus champion, Dani Samuels, said the mosque shooting had led to her decision to pull out.

English diver Peter Waterfield, a previous gold and silver medal winner, said he was putting his family first and would not put himself at risk by travelling.

"I have a wife and two young children who were very concerned about me attending the event and this decision is one that we have made as a family. I hope that people will understand and respect this," he said.

Among the potential banana skins India must still negotiate are a court verdict due out on Tuesday on the hugely contentious Hindu-Muslim dispute involving the religious site at Ayodhya, in Uttar Pradesh, which has claimed thousands of lives in recent years. Security forces around the country have been placed on alert as a ruling is delivered on whether a Hindu temple or Muslim mosque can be built there.

The task of keeping order will be made more difficult by the decision to assign at least 40% of police in the capital to Games security, including inspectors in charge of anti-terrorism squads.

But Delhi's police commissioner, YS Dadwal, said that he was completely satisfied with security arrangements. "I assure international athletes that there is foolproof security for the Commonwealth Games," he said. "There is no doubt over it."