The immigration minister blocked at least two British citizens on Twitter when they asked for her assistance after the Home Office failed to respond to their complaints or appeals from their MPs.

Caroline Nokes’ action, which means the people concerned are unable to read her tweets or contact her, were described by a leading immigration lawyer as suggesting “complete indifference”.

Stephen Buck was blocked from following Nokes or seeing her tweets on 11 August after he sent her three tweets in four months, asking for help to prevent his long-term partner, Rusty Goodall, from being deported to Australia. It took the Home Office 13 months to refuse Goodall’s application to extend his visa, during which time the couple received no update on his case.

“I was nothing but polite in my approaches, but having tried all other avenues available to us (ie contacting the Home Office directly, asking our MP for help) and still feeling as though we were in a position where nobody was doing anything and nobody cared about us, contacting Nokes on Twitter felt like the only option left to try and get somebody in power to listen,” Buck said.

“The fact that the only response to these pleas to one of the few people who could make a difference in our case was to block me, was truly upsetting, frustrating and insulting.”

John Holden, a British citizen who lives in the UK with his Filipino wife, son and three adopted children, was blocked by Nokes on the same day as Buck after also asking for help.

“The Home Office have refused to issue my British children with British passports: they say we need to change the children’s Philippine passports to their new adopted surnames first,” he said.

“The problem is that the Philippine authorities won’t do that unless we take the children out of school and return to the Philippines for a process that could take up to 18 months, during which I would have to readopt children who are already mine and are already British.

“The Home Office has been completely deaf to my appeals and complaints, even though they’re acting against their own guidelines.

“The minister’s Twitter page is a platform that enables two-way communication, and I did nothing more than politely – and always respectfully – request her to meet with my MP.

“My appealing directly to the minister was nothing more than a desperate plea when the feeling of helplessness became overbearing. To be blocked for no apparent reason merely compounded the feeling of despair at a time when it felt all hope was lost.”

Syed Naqvi, the head of the immigration department at ITN Solicitors, said: “It is concerning that an applicant has been barred from contacting Ms Nokes on Twitter for simply requesting information pertaining to his case. Ms Nokes’ actions are overzealous and certainly not acceptable in a democratic society.

“Her actions also smack of a complete indifference to the problems faced by the applicants and their families. How can she claim to be able to address the problems with our immigration system when she is not even prepared to listen to its service users?”

Andrew Chadwick, a professor of political communication at Loughborough University and the director of the Online Civic Culture Centre, described Nokes’ decision to block Bucks and Holden as “questionable”.

“There is a strong culture of transparency and publicness on Twitter,” he said.

“Effectively, when a politician blocks a member of the public – and in this case one who appears to have been acting in a civil way – they’re saying they simply don’t want to hear what the person has to say, and they’re not interested in that person’s problems, under any circumstances.

“That seems to me to be questionable behaviour for a politician. Surely they can do better.”

The Home Office said: “Twitter is not an appropriate medium to discuss individual cases. Caroline Nokes passed on correspondence through the correct channels.”