England's contact tracers have only reached about 50% of people who have been in close contact with someone with Covid-19 in an area of Lancashire where new cases are rising.
The figure was revealed by Prof Dominic Harrison, public health director of Blackburn with Darwen Council.
He warned of "exponential growth" of new infections if the system did not become more efficient.
It is not clear why the contacts provided were not able to be reached.
A leaked report, seen by the Independent, suggested that fewer than half of contacts were reached in Oldham, St Helens, Manchester and Rochdale.
Speaking to BBC Radio 4's Broadcasting House programme, Prof Harrison said that Blackburn with Darwen in Lancashire, which he oversees, faces a "rising tide" of infections.
"The key issue here is that 40% of people who are infected by someone with Covid-19 who goes for tests because they have symptoms, will be infected by them before they have those symptoms," he said.
"So, there's a 48 hour window which is critical to get the contacts of the first case contacted, and if we don't get them contacted, and if they don't then get tested and self-isolated, and they then have symptoms, we do risk the spread progressing."
He called for testing and tracing to be carried out at a local rather than national level, and for Public Health England to share more data with local authorities.
Prof Harrison said PHE had only begun sharing data about the postcode areas in which new infections were being registered on 29 June.
"That has made a great difference in three weeks for us in being able to identify what our local outbreak issue is," he said.
"Had we had that data much earlier in this pandemic, I think we could have made progress much more rapidly."