It comes as leaked documents revealed a backlog of 185,000 tests, with many being sent to German and Italian laboratories for processing, according to the Sunday Times.
Last month saw two Portsmouth residents living less than 30 minutes away from two Covid-19 testing sites in the city being directed to book a test in Manchester instead.
Last week another person was told to travel to Aberdeen – but this slot then vanished.
Portsmouth has a rate of 13.5 cases per 100,000 for the week to September 10, with 29 new cases in that period. This is up from a 7.4 rate in the week before, with 16 cases.
The NHS Test and Trace system’s capacity is ‘the highest it has ever been’, according to a spokesman from the Department of Health and Social Care.
He told The News: ‘But we are seeing a significant demand for tests including from people who do not have symptoms and are not otherwise eligible.
‘New booking slots and home testing kits are made available daily for those who need them and we are targeting testing capacity at the areas that need it most, including those where there is an outbreak, and prioritising at-risk groups.
‘Our laboratories are processing more than a million tests a week and we recently announced new facilities and technology to process results even faster.
‘If you do not have symptoms and are not eligible to get a test you can continue to protect yourself if you wash your hands, wear a face covering and follow social distancing rules.’