People particularly struggled when ordering tests from the Government website and collecting them from pharmacies.
More than a fifth of adults in Britain had difficulties getting lateral flow tests earlier in January, figures suggest.
Some 22% told the Office for National Statistics (ONS) they had struggled to order or pick up a rapid-result test in the past seven days.
The most common places difficulties were experienced were when ordering on the Government website for home delivery (68%) and collecting from pharmacies (60%).
The majority (85%) said the difficulties did not stop them from doing anything they had planned.
The ONS analysed responses from 3,293 people between January 6 and 16 as part of its Opinions and Lifestyle survey.
It found 61% of adults said they had taken a lateral flow test in the last week – up from 57% in December 15 to January 3.
The figures also show that one in 10 adults reported self-isolating because of coronavirus in the past seven days.
This is up from 7% in the previous survey period and 5% prior to Plan B measures.
It is comparable to the proportion self-isolating this time last year, when the country was in its third national lockdown.