Cllr Sweeney said: "To have cancelled 50 trains, with the limited services that we have, in a month is just beyond belief, the excuse is unprecedented levels of sickness. The record on late trains is appalling."
The deputy council leader said the quality of the rolling stock, with some 56-year-old Class 37 engines, is "abysmal".
He said: "It is all pie in the sky promises - there will be jam tomorrow. Northern has been trying for nine months; I thought we were getting somewhere with them and then all we are seeing is delays with trains and delays with rolling stock."
Councillor Bill McEwan seconded the motion and spoke about the health worries of residents who live near to Barrow rail station due to fumes and noise pollution.
Cllr McEwan said: "This issue has dragged on for so long. The residents at the Griffin estate have had to suffer ongoing levels of noise at all times: Midnight, at 2am, 4am and 6am. This is just not on. They can't open their windows in summer time because of the fumes and they are woken up at all hours."
Councillor Frank Cassidy said: "Our local rail service appears to be heading for the buffers. People who use the Furness line are fed up with out-of-date rolling stock, they are sick of cancellations and tired of excuses."
Cllr Cassidy said promises of more carriages, better trains and extra services had not been kept and said the service was "woeful".
He said the RMT union had told him that there is "not an adequate number of core staff to deliver a robust service in Barrow".
Cllr Cassidy said huge investment was surging into the area but the area "cannot go forward with confidence if we are served by a rail infrastructure that is so appalling and out-of-date.
"It's time our rolling stock stopped being a laughing stock".
The council agreed that it "regards Northern Rail's performance and attitude as completely unsatisfactory" and Cllr Pidduck will write to the managing director and chairman of Northern Rail, and write to Transport North, the secretary of state for transport and the Office for Rail Regulation.
He will also raise the problems with the Cumbria Leaders Group with a view to joint lobbying.
A spokesman for Northern said: “We understand the frustrations of passengers in and around Barrow and South Lakes who have recently experienced delays to their journeys.
“Unfortunately, as a result of unprecedented levels of sickness absence, we experienced a number of staff shortages in November and December which had a significant impact on the service we were able to offer to our customers.
“Of course, we do plan for and seek to mitigate certain levels of absence, but those we experienced towards the end of 2016 were over and above those which would normally be expected.
“Staffing levels have since returned to normal and we have recorded notable improvements in terms of the number of services being run to time in the Barrow area."
