NHS England figures show the median waiting time for non-urgent elective operations or treatment at Bedfordshire Hospitals NHS Foundation Trust was 13 weeks at the end of January – up from 12 weeks in December.
This was also more than the average 11-week wait a year previously.
There were 70,046 patients on the waiting list in January – up from 67,922 in December, and 44,125 in January 2021.
Of those, 2,424 had been waiting for longer than two years.
Nationally, 6.1 million people were waiting to start treatment at the end of January.
Health Secretary Sajid Javid recently announced NHS reforms, which include paying for patients who have been waiting the longest to travel to less busy hospitals or private facilities for care.
But Siva Anandaciva, chief analyst at the King’s Fund health think-tank, said these promises will "ring hollow if hospitals throughout England continue to flash red".
He added: "Staff shortages remain the rate-limiting factor in the Government’s ambition to reduce the backlog.
"Without a fully-funded workforce plan, key targets will continue to be missed and people will continue wait longer for the care they need."
Separate figures show 1.5 million patients in England were waiting for a key diagnostic test in January – a rise on 1.4 million in December.
At Bedfordshire Hospitals Trust, 15,994 patients were waiting for one of 15 standard tests, such as an MRI scan, non-obstetric ultrasound or gastroscopy at this time.
Of them, 5,093 (32 per cent) had been waiting for at least six weeks.
There is no further breakdown between the two hospitals - Bedford and Luton & Dunstable.
The Nuffield Trust said the latest national figures on the state of the NHS make for "sobering reading", particularly amid a rise in hospital admissions for Covid-19.
Sarah Scobie, deputy director of research at the think-tank, said: “Behind all of these figures are thousands of individual stories of pain and suffering, set against a backdrop of burnt out and overworked healthcare staff.
"The question for the Government is how far the reforms proposed will really touch the sides in the face of such long and growing waiting times.
"A renewed wave of the virus just as health and social care services are struggling to get back on their feet could be perilous for any hopes of recovery.”
Other figures show cancer patients at Bedfordshire Hospitals Trust are not being seen quickly enough.
The NHS states 85 per cent of cancer patients urgently referred by a GP should start treatment within 62 days.
But NHS England data shows just 69 per cent of patients received cancer treatment within two months of an urgent referral at Bedfordshire Hospitals Trust in January.
That was up from both 61 per cent in December, and 67 per cent in January 2021 last year.
The Department of Health and Social Care said its plan to tackle the Covid-19 backlog is backed by a multi-billion pound investment over the next three years, and it will also publish a 10-Year Plan on cancer.
A spokeswoman added: “We will deliver new surgical hubs and at least 100 community diagnostic centres to help patients get the surgery they need and earlier access to tests – including for cancer – delivering an extra nine million scans, checks and procedures by 2025.”