David Lammy has said he plans to appoint an envoy to deal with “complex detention cases” involving Britons abroad and give them a legal right to consular access.

After the Guardian’s reporting on detained Britons, the foreign secretary said he had been “looking hard” at the thousands of cases a year involving people who require consular assistance.

“I do hope to announce an envoy, a special … an individual who will deal with more complex detention cases,” he told the foreign affairs select committee on Wednesday.

Lammy paid tribute to consular staff but said that in “more complex cases” there were issues that required a “tightening of grip” by the Foreign Office. Asked about the Labour manifesto commitment to give UK citizens a legal right to consular access when they run into trouble overseas, he said: “We will be coming forward with plans.”

“I have been looking hard at the 28,000 people at any one time that come through our system … It’s varied, from someone who was arrested for being drunk in Magaluf to, sadly, there have been high-profile cases where British citizens have sadly lost their lives for varied reasons abroad,” Lammy told MPs.

The Foreign Office says that in any given year it supports about 20,000-25,000 British nationals and their families, including about 4,000-5,000 detained or arrested abroad. Appointing a special government envoy to help secure the freedom of Britons detained for years without trial would fulfil a promise Lammy made in opposition.

The Guardian reported on fears of pushback against the envoy plan by senior UK diplomats, who worry it would affect relationships with other countries and trade deals.

Earlier on Wednesday, Lammy met the family of Alaa Abd el-Fattah, the British-Egyptian software developer and democracy activist who is Egypt’s most high-profile political prisoner. He was due to be released in September but has not been freed, and his mother, Laila, is on hunger strike.

At a press conference, Laila Soueif and her two daughters Sanaa and Mona said they felt listened to by Lammy but that he had made no concrete promises and they wished the meeting had happened months ago.

“He listened to me, I hope my message got through. My main message was that I’m on hunger strike, I’m not about to break my hunger strike until Alaa is released,” Soueif, who has lost 16kg (35lbs) since starting her strike, told the Guardian. “We’ve had a lucky break by the fact that my body has been so resilient and my body has not collapsed.”

To date, Abd el-Fattah has yet to have a visit from the British consulate. “Things like consular access can be pushed on a ministerial level and I still want to see progress on that,” said Soueif, adding that it would “make a lot of difference” for her son’s morale.

Sebastien Lai, the son of detained media mogul and pro-democracy activist Jimmy Lai, was in the room for Lammy’s first committee hearing as foreign secretary. His father, whose trial resumed last week after repeated delays, has been in a Hong Kong jail cell for almost four years. He is being held in solitary confinement and faces a life sentence if convicted.

Asked about Canada, the US and Australia getting several of their detained citizens out of China in recent years, Lammy said the UK had been held back by the “lack of engagement” with Beijing under the Conservatives.

Lai’s supporters have said the UK government’s support for him has been “ridiculously” lacking compared with the US, Canada and Australia, which have lobbied for him. Keir Starmer raised Lai’s case at his bilateral meeting with Xi Jinping, the Chinese president, on the margins of the G20 summit in Brazil earlier this month.