The Royal Devon University Healthcare Foundation Trust is not meeting NHS cancer targets, figures show.
A leading charity has said the Government needs to pull cancer care out of a "permanent state of crisis".
New figures from NHS England show cancer patients at the Royal Devon University Healthcare Foundation Trust are not being seen quickly enough.
The NHS states 85% of cancer patients with an urgent referral should start treatment within 62 days.
But NHS England data shows just 59% of cancer patients urgently referred to the Royal Devon University Healthcare Foundation Trust in January began treatment within two months of their referral.
That was down from both 65% in December, and 66% in January 2023.
The proportion of patients in England waiting longer than 62 days in January from an urgent suspected cancer referral or consultant upgrade to their first definitive treatment for cancer was 62%, down from 66% in December and below the target of 85%.
Minesh Patel, head of policy at Macmillan Cancer Support, said these delays "can’t go on".
"Healthcare professionals are doing all they can but are working in a permanent state of crisis," he added.
"If the UK Government acts now, we can turn this around and ensure our cancer system is fit for purpose in the years to come.
"We need a long-term cancer strategy in England that provides the investment and focus needed so that everybody with a cancer diagnosis gets the timely and quality care they deserve."
Professor Pat Price, who co-founded the #CatchUpWithCancer campaign, described the situation as "a disaster for cancer patients" and called for "a radical new cancer plan and a clear implementation plan to improve waiting times and cancer survival".
A separate NHS target aims for 75% of patients with suspected cancer to be diagnosed or have the disease ruled out within 28 days – at the Royal Devon University Healthcare Foundation Trust, 73% of patients were seen within that timeframe.
Across England, 71% of patients urgently referred were given a conclusive diagnosis, down from 74% the previous month and below the target of 75%.
GPs across England made 250,000 urgent cancer referrals in the month – a rise from 220,000 in December and 228,000 in January 2023.
An NHS spokesperson said: "The NHS is seeing and treating record numbers of people for cancer, with 30% more people being treated last year than in 2015-16 and almost 3 million people receiving potentially lifesaving cancer checks in the last 12 months, ensuring more people than ever before have been diagnosed at an early stage and cancer survival is at an all-time high.
"It is vital that people come forward if they are concerned about cancer symptoms – getting checked early saves lives."