Experts have blamed these delays on a lack of funding, meaning hospitals do not have the necessary staff or equipment to keep up with the demand.
NHS trusts provide information on how long patients have been waiting for 15 key tests at the end of each month.
The procedures are used to diagnose a wide range of diseases and conditions, including cancers, heart failure, hearing problems and sleep disorders.
According to NHS rules, after a patient is referred for one of the tests, they should have it done within six weeks.
NHS England data shows that 8,320 patients at Doncaster and Bassetlaw Teaching Hospitals NHS Trust were waiting for one of the tests at the end of June.
But 111, 1.3 per cent, had waited six weeks or more which is just above the national target of one per cent.
And of those, seven were kept waiting for at least 13 weeks.
The most common type of test for which patients saw delays was peripheral neurophysiology, which tests the function of the nerves and muscles – for which 48 people waited at least six weeks.
The next most delayed test was audiology, which assesses a patient’s hearing and balance whereby 24 patients endured the same hold-up.
And 19 people were left waiting the same length of time for urodynamics, which can be used to help identify why a patient finds it hard to empty their bladder.
The rate of patients at the trust waiting six weeks or more has risen slightly – 0.7 per cent experienced such a delay in June 2018.
The trend at the trust reflects that across England, where 3.8 per cent of patients had waited at least six weeks for the tests at the end of June – the figure stood at 2.9 per cent the previous June.
A spokesman at Doncaster and Bassetlaw Teaching Hospitals said: “Although the Trust performs very well when compared to national performance we are always striving to improve and in June the Trust introduced additional capacity in neurophysiology, audiology and urodynamics to ensure we are able to achieve the six week standard for our patients.
“As a result, just one month later, more than 99 per cent of our patients were offered a test within the targeted time; exceeding the national standard.
“We continue to monitor and manage this carefully to ensure all patients are offered prompt diagnostic tests, enabling them to receive the best quality care and treatment.”