Data from the Department for Health and Social care shows 2,454 people who tested positive for Covid-19 in Portsmouth were transferred to the Test and Trace service between May 28 and November 11.
That means 507 new cases were transferred in the latest seven-day period.
Contact tracers ask new patients to give details for anyone they were in close contact with in the 48 hours before their symptoms started.
This led to 6,428 close contacts being identified over the period – those not managed by local health protection teams, which are dealt with through a call centre or online.
But just 59.6 per cent of those were reached, meaning 2,596 people were not contacted or did not respond.
That was slightly up from the 59.5 per cent reached in the period to November 4 – but the target is 80 per cent.
Two-thirds of contacts of people with coronavirus in the Hampshire County Council area were reached.
This was fewer close contacts of people than the previous week, and was a record number of new positive cases for the area.
Data from the Department for Health and Social care shows 8,965 people who tested positive for Covid-19 in Hampshire were transferred to the Test and Trace service between May 28 and November 11.
That means 1,907 new cases were transferred in the latest seven-day period – the largest increase since the regime began.
Some 23,623 close contacts were identified.
But just 66.7 per cent were reached, meaning 7,855 people were not contacted or did not respond.
That was slightly down from the 67.2 per cent reached up to November 4, but above the 62.7 per cent average across the south east as whole.
Across England, 58.9 per cent of contacts not managed by local health protection teams were reached and told to self-isolate by NHS Test and Trace in the latest week to November 11.
Local health protection teams deal with cases linked to settings such as hospitals, schools and prisons.
The contact tracing rate including these cases was 60.5 per cent – in line with the week before.
Around 157,000 new cases were transferred nationally in the week to November 11. As with Hampshire, this was the highest weekly number since NHS Test and Trace was launched.