The petition, which, at the time of writing, had 147,601 supporters, has been shared on change.org
Once it reaches 150,000 signatures, it will become one of the top signed petitions on the website.
Organised by user "S M Y" and aimed at the UK parliament and the prime minister, the description said: "Dear Boris Johnson... I am disgusted with how expensive it is for my family to go abroad for the first time in over two years since this pandemic started.
"You have made [testing] mandatory, even for fully vaccinated travellers, yet you are forcing us to pay expensive private companies.
"We should not have to pay for this. If this is mandatory then we should be able to have the tests on the NHS. I know that I do not stand alone in this and we urge you to change the testing to make it easier for fully vaccinated people to travel."
