Bradford has the worst Covid-19 contact tracing rates in England, according to Department of Health figures.
Just 42% of contacts of people who tested positive were reached through NHS Test and Trace in the week ending 2 September.
It falls behind the national average of 69% and the government's target of 80%.
The council blamed a lack of government funding for local test and trace, while the government said the system was reaching the majority of people.
Other places with low contact rates include Peterborough with 46%, Blackburn with Darwen with 48%, and Kirklees and Nottingham with 49%.
North Tyneside had the highest number of people being traced during the same period, standing at 74%.
Contact tracing is considered vital to help stop the spread of the virus with the prime minister making it a legal requirement that pubs and restaurants take people's details.
The new requirements were announced alongside enhanced coronavirus measures making gatherings of six or more illegal and enhanced police powers to enforce the rules.
Bradford Council said in the seven days to 8 September, the infection rate in the district was 71 cases per 100,000.
The authority has now brought in a team of specialist tracers but council leader Susan Hinchliffe said a lack of funding for local test and trace had hampered their efforts.
She said: "They [the government] seem to be able to find money to pay for a national test and trace but when it comes to local authorities money is still not there.
"We shouldn't be having to pay for that as a local authority which is already stretched in terms of finances."
Contact tracing rates for the rest of Yorkshire also fall below the 80% target, including Sheffield at 52% and Hull at 54%.
The government said since the system was launched in June, 358,294 people had been reached and where contact details were shared with those testing positive, 87% were traced.
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