Surge testing has begun in parts of Kirklees - which has the fourth highest coronavirus rates in the country.
People are being urged to visit one of six testing sites - three of them new mobile units - even if they don't have symptoms.
Council and NHS staff have started going door-to-door in parts of Dewsbury and all people aged over 11 in Savile Town and Thornhill Lees are being asked to take PCR tests and all adults offered vaccinations, Kirklees Council said.
It comes hours after the government's advice not to travel into or out of the area was withdrawn and Kirklees director of public health said there are no local restrictions.
The Department of Health and Social Care said it would instead be issuing advice to those living in the areas after ministers were accused of bringing in rules on socialising and travelling "by stealth".
It insisted lockdown measures were not being put in place.
A Government spokesperson said: "We will be updating the guidance for areas where the new Covid-19 variant is spreading to make it clearer we are not imposing local restrictions. Instead, we are providing advice on the additional precautions people can take to protect themselves and others in those areas where the new variant is prevalent."
This includes urging people to meet outdoors rather than indoors, staying two metres apart from people not in the same household, and minimising travel in and out of the area.
The spokesperson said: "These are not new regulations but they are some of the ways everyone can help bring the variant under control in their local area."
The move comes after a day of confusion over the measures, which appeared on the Government website on Friday, but without an official announcement.
The Government said the recommendations to the hotspot areas were first issued on May 14 - with the Prime Minister urging people to be "extra cautious" - before being "formally" published online last week.
No 10 stressed that the guidance was "not statutory" and the Government wanted to move away from "top-down edicts" as lockdown eases.