Theresa May has been urged to confirm she will put human rights reform on her agenda when she meets Saudi and Bahraini leaders on Tuesday, after announcements on her two-day trip to the Gulf were squarely focused on trade and security.

Rights campaigners in Bahrain argue that although the UK has been assisting Bahrain with judicial and police reform since 2012, current levels ofengagement on rights issues have not prevented crackdowns on journalists and pro-democracy activists in the country.

May said: “I think the UK has always had the position, and we continue to have the position, that where there are issues raised about human rights, where there are concerns, we will rightly raise those.

“I already have done in some of the meetings I’ve already had in my time as prime minister, and we will continue to do that. But I think what’s important is that because we have the overall engagement, we are able to raise those issues around human rights.”

Asked about Saudi Arabia’s record in the Yemen conflict, May – who is due to meet King Salman later on Tuesday – said: “If any allegations are raised about breaches of international humanitarian law … we’re very clear those should be properly investigated and encourage the Saudi Arabians to investigate those, and to ensure that any lessons are learned from those investigations.”

Before her speech on Wednesday at the Gulf Co-operation Council (GCC) summit, May announced the establishment of the first joint UK-GCC counter-terrorism working group, with a focus on border and airport security and blocking terrorist financing. The UK will advise on more effective screening at airports in the region, with the aim of improving the tracking of potential terrorists.

On her first morning in Bahrain, the prime minister will speak to 900 British troops on board HMS Ocean in Khalifa bin Salman Port in Bahrain. The vessel provides the command platform for operations in the Middle East, including directing US Task Force 50, the Americans’ Gulf fleet.

As well as the UK government’s £3bn defence fund for the region over the next 10 years, where more British warships, aircraft and personnel are deployed than anywhere in the world, more MoD staff are to be deployed to the region, including a new permanent defence staff in Dubai and a military officer embedded with Bahrain’s bomb disposal unit.

Three UK cybersecurity experts have been appointed to advise Gulf institutions and training on countering terrorist financing. Their first workshop will take place in Qatar next week.

However, the commitment to helping Gulf nations strengthen their security apparatus and intelligence-gathering is likely to raise concerns from NGOs that any new surveillance capabilities would also be used to monitor pro-democracy activists and journalists.

Labour and Lib Dem MPs called the trip “the shabby face of Brexit” and said the prime minister must not let the desire for greater co-operation override concerns about crackdowns on journalists and protesters, as well as the conflict in Yemen.

Sayed Ahmed Alwadaei, director of advocacy at the Bahrain Institute for Rights and Democracy, said: “We are deeply concerned that this security co-operation against terrorists may apply to human rights activists and critics to the regime. Bahrain labels human rights activists as terrorists and revokes their nationality.”

Fabian Hamilton, shadow Middle East minister, said: “I am not convinced that concerns for human rights will be prioritised over a trade deal, given the government’s obsession with having to show that the UK can cope on its own once it leaves the EU. I am concerned at the seeming complacency shown by Boris Johnson’s comments on the Saudi-led bombing campaign in Yemen on Sunday.” Tom Brake MP, Liberal Democrats’ spokesman for foreign affairs, echoed the concerns. “The PM’s desperate drive to boost UK exports must not come at the expense of the UK’s commitment to upholding human rights around the world,” he said. Turning a blind eye to human rights abuses in Bahrain, Saudi Arabia or Yemen will do long-term damage to the UK’s international standing.”

May, who was greeted on her arrival in Bahrain on Monday night by King Hamad bin Isa al-Khalifa, is said to be keen to deepen regional security ties, which Downing Street said had already saved British lives, pointing to the October 2010 “printer bomb” scare at East Midlands airport on a flight bound for the US, which was caught by security forces after being picked up by Saudi intelligence.

Speaking before her visit to HMS Ocean, the prime minister said the security of Gulf countries and the UK were intertwined. “Now more than ever, Gulf security is our security,” she said. “And it’s not just about military power – we also need to work together to respond to new and diversifying threats. So, on my visit here, we are agreeing new cooperation to do more to prevent radicalisation and to tackle terrorism.

“In all of these ways, I am determined to step up our defence and security partnership to provide greater confidence and stability to the region and to keep our people safe in an ever more dangerous world.”

On Tuesday, May will have bilateral meetings with three different Gulf leaders – the king of Saudi Arabia, the emir of Kuwait and the prime minister of the United Arab Emirates – as well as host a reception for young Bahraini leaders. She will dine later with all six Gulf leaders before her speech at the GCC on Wednesday, where she will become the first woman to address the summit.

Over the weekend, rights groups including Reprieve, Human Rights Watch, Index on Censorship and the Bahrain Institute for Rights and Democracy wrote to May asking her to change her tactics for engagement with Gulf leaders.

May has been urged in particular to call for the release of the pro-democracy campaigner Nabeel Rajab, who faces 15 years in jail for criticising Bahrain’s role in the war in Yemen and for an article he wrote in the New York Times about the country’s crackdown on activists, which led to him being charged with defaming the state. The US government has called for Rajab’s release, but the Foreign Office has not, saying simply that it is monitoring the case.