A total 301,076 cases were passed to investigators for checks on whether they were self-isolating as the coronavirus delta variant took hold.
More than one million people arrived in England and Northern Ireland from amber list countries from March 17 to May 31.
Figures from a Freedom of Information request submitted by the BBC show almost a third of these cases were referred for investigation.
Labour’s shadow home secretary Nick Thomas-Symonds said the data “confirm our worst fears” about the government’s “lax border policy” and accused the Home Office of gross negligence.
However, the government denied the accusation and said the appropriate measures were taken.
A spokesperson said: “The Home Office looks to visit all individuals referred to us by NHS Test and Trace who are required to isolate at home following international travel.
“We visit over 99 per cent of the cases referred to this service by NHS Test and Trace.”
The government introduced new rules for international arrivals earlier this year to combat the spread of coronavirus and emerging variants.
Those coming from amber list countries were required to quarantine for ten days and show proof of negative Covid tests.
Call handlers at the Department of Health and Social Care (DHSC) contacted the arrivals and asked if they were sticking to the rules.
Cases were referred to Border Force investigators and the police where people hung up, suggested they would break the rules, refused to cooperate or did not answer after three call attempts.
Officers would then try to visit them at home to make sure they were complying.
The Evening Standard has contacted the DHSC for comment.