The people on the island claim it symbolises how they are treated as second-class citizens when it comes to provision of both emergency cover and telecommunications.
Mull Community Council has resolved to fight the island's corner with more determination in future for the near 3000 residents, whose road system is largely single track.
The two GPs based in Tobermory in the north of the island are a couple and have a separate surgery number for during the day and one for their house phone.
Argyll and Bute councillor Mary-Jean Devon, of Tobermory, became aware of the problem only when chatting to the doctors.
She said: "I was at the doctors and they told me that they had been without their house phone since May 23.
"I asked if that was the phone the hospital in Craignure would contact them on or NHS 24, and they said yes. I didn't even ask about their mobiles because on this island reception can be fine one day and not the next.
"So they had to give the receptionist's number to the emergency services in case they were needed during the night. I don't think they were, but I was appalled."
Ms Devon said she also knew of a couple in a remote part of Mull, where there is no mobile reception, who were without their phone for two weeks.
"The husband has a heart condition and they would have to drive two miles to get reception to phone a doctor. In the 21st century it is totally unacceptable."
Internet connection was also poor over much of the island, she said, even preventing the mobile dentist who serves Mull, Coll and Tiree from visiting the south of the island because he cannot access his records online.
Meanwhile, in Pennyghael in the Ross of Mull, community councillor Fiona Brown said: "There are two ambulances on the island and two crews, but only one crew is on at any given time. We have already had an incident when it was more than two and a half hours to get to Pennyghael and it is another good half-hour in an ambulance to get right down the Ross of Mull to Fionnphort."
She added that the two GPs who cover the Ross of Mull would leave at the end of September, as would one of the two in Salen, out of the island's total of six GPs.
"The situation here is very worrying because we are not just talking about Mull but Iona and the islands of Ulva and Gometra as well," she said.
A spokesman for the Scottish Ambulance Service said demand for ambulances was constantly analysed and the service was aware of concerns on Mull, but added: "Ambulance personnel on the island are supported by an air ambulance helicopter that is available for immediate response 24/7 and we are currently evaluating the potential to increase the number of First Responder schemes on the island."
A BT spokeswoman apologised about taking longer than the usual three working days maximum to restore the doctors' standard residential line.
She said: "Engineers began investigating within the usual time limit but were not initially able to trace the fault. Once it was tracked to the local exchange, work was carried out there. When this did not restore service, a second fault was found in an aerial cable. Service was restored on Thursday June 5."
In addition, an NHS Highland spokesman said a replacement for one of the Ross of Mull GPs had already been recruited.