One of the four jailed al-Jazeera journalists in Egypt no longer has full use of his arm after being denied proper medical treatment in prison for a shoulder injury suffered before he entered custody.

In his first trip to a civilian hospital since his arrest in late December, the Canadian-Egyptian journalist Mohamed Fahmy showed friends and family on Saturday that he could not move his right arm more than a few centimetres.

Driven to hospital by an escort of balaclava-wearing police officers, Fahmy used his rare contact with the outside world to ask to be given more regular access to his lawyer, who he meets for only 45 minutes before a court appearance, and for the court's sessions to be held more regularly than once every three weeks.

An ex-CNN producer, Fahmy also requested to be allowed more than one hour each day outside his windowless cell, which he shares with fellow al-Jazeera journalists Peter Greste and Baher Mohamed.

They have been placed next door to two leading allies of the former president Mohamed Morsi – the head of Morsi's Muslim Brotherhood, Mohammed Badie, and his one-time prime minister, Hisham Kandil.

The three journalists were arrested in their hotel rooms on 29 December and accused of spreading misinformation about Egypt and aiding terrorists – charges they describe as absurd. A fourth, Abdullah Elshamy, has been detained since August.

The Egyptian state claims that their coverage distorts Egypt's image in order to help Morsi's Muslim Brotherhood, which it has designated a terrorist group. But globally the cases are seen as an attack on free speech and have sparked widespread outcry.

In his appearance at hospital, Fahmy said Greste and Mohamed were in good spirits and were now allowed to read newspapers, which helped to alleviate the boredom of prison.

Fahmy appeared upbeat himself, joking with family members in between two scans on his injured arm, and saying the experience would be good material for a book.

"Let's go home," he quipped to a police officer as he left again for prison.

But his family stressed that Fahmy needed to return to hospital as soon as possible. "He should be released on bail to allow him to get proper treatment," said Adel Fahmy, the journalist's younger brother.

The three journalists are due back in court on Monday.