The Formula One teams want the sport's governing body to cancel – or at least postpone – the Bahrain Grand Prix, which is scheduled for 22 April, because of increasing safety concerns amid ongoing protests in the kingdom, according to a leading member of one of the teams.

The team member, who would not be named but who said his views were representative, told the Guardian: "I feel very uncomfortable about going to Bahrain. If I'm brutally frank, the only way they can pull this race off without incident is to have a complete military lockdown there. And I think that would be unacceptable, both for F1 and for Bahrain. But I don't see any other way they can do it."

Until now the teams and sponsors have kept quiet, maintaining a united front and leaving the big decision to the men who rule the sport. And Jean Todt, the president of the Fédération Internationale de l'Automobile (FIA), the sport's governing body, and Bernie Ecclestone, the commercial rights holder, have insisted that the race will go ahead.

But the team principal who broke rank added: "We're all hoping the FIA calls it off. From a purely legal point of view, in terms of insurance and government advice, we are clear to go. But what we find worrying is that there are issues happening every day."

Last year's grand prix was cancelled after more than 40 people died, many after being tortured, following Shia-led protests against the Sunni ruling family.

British MPs voiced worries at the weekend in the wake of fresh protests and the growing concern for the condition of the jailed activist Abdulhadi Alkhawaja. Last Friday, security forces fired tear gas and water cannon at thousands of Alkhawaja supporters. On Saturday his daughter Maryam described him as being ready to die. Zainab, another daughter, was also detained.

"We have a lot of people. Our first and foremost priority has to be our employees. And their families," the team principal told the Guardian. "That's what concerns us most, even though we've not said anything about it. It seems to me that while there has been some political progress in Bahrain they're not quite ready. The best thing would be for the race to be postponed until later in the year, or even cancelled.

"But that is a decision that must be made by the FIA, FOM [Formula One Management] and the commercial rights holder. I never anticipated a decision being made until the week before China. I believe Jean Todt is in China, which is interesting."

The fact that this Sunday's race, in Shanghai, and the Bahrain GP are scheduled back-to-back has complicated travel arrangements, with many half expecting the Bahrain event to be put back. Some teams have reportedly been issued with two return tickets, one home via Bahrain and the other directly home.

Last week, in the Guardian, the former F1 world champion Damon Hill, a Sky Sports commentator who had spoken out in favour of the race taking place earlier in the year, called for a rethink by the FIA. Hill, who last year called for the race not to be rescheduled following its cancellation for safety reasons, added at the weekend: "F1's chiefs must not act like they do not care. I think at the moment it is hotting up, which is not a good state of affairs to be wanting to go to Bahrain, when it is actually getting more inflamed."

The protest campaign in Bahrain has been intensifying around Sunday's (8 April) first anniversary of Alkhawaja's arrest. He is now on his 60th day of hunger strike and reportedly close to death. He has spent the past year in prison after receiving a life sentence in a Bahraini security court on a charge of "plotting to overthrow the monarchy" — supporters say on the basis of a confession obtained under duress. On Sunday Bahrain rejected a request from the Danish government to transfer Alkhawaja, 52, to Denmark, where he also has citizenship.

John Yates, former assistant commissioner in the London Metropolitan Police Service who is advising the Gulf kingdom's interior ministry, told the Associated Press: "It is very much hoped that the policing [of the grand prix] will be low key and discreet. But if there are problems, they … must be able to escalate their response if need be." He said he expected some protests would be allowed but warned that anyone trying to shut down the race would be treated harshly. "If people want to protest lawfully and give proper notice, as they have to, then they will be allowed to protest," Yates said. "But you can't have a protest that shuts off every road and doesn't allow people to get to the grand prix circuit. That would be absurd. They can be allowed to protest in certain places where it doesn't cause huge disruptions and their message can get across."

Hosting the grand prix is an issue of enormous prestige for the Manama government, which was dismayed at the blow to its carefully nurtured reputation for stability when it was cancelled last year because of the unrest. Bahrain is seen in the Middle East as the most striking failure of the uprisings of the Arab spring, where the protests in February and March 2011 were crushed by the western-backed monarchy with the help of an armed intervention force led by Saudi Arabia.

The US and Britain have been accused of hypocrisy in turning a blind eye to repression though both governments have urged King Hamad to follow the recommendations of a officially appointed Bahrain Independent Commission of Inquiry, which found that his government was guilty of "excessive force" in its crackdown against protesters.

According to official figures the UK government approved the sale of military equipment valued at more than £1m in the months following the violent crackdown. They included licences for gun silencers, weapons sights, rifles, artillery and components for military training aircraft.