The government has advised against all but essential travel in eight areas of England where the Indian variant is spreading fastest.
Officials said areas including Bolton, Leicester, Kirklees and the London borough of Hounslow were hardest hit and people there should not meet indoors.
People should avoid travelling into and out of the eight areas, with Bedford, Blackburn with Darwen, Burnley and North Tyneside also on the list.
People in the eight areas should also be tested twice a week, according to the Government advice.
The change to the guidance, which is not law, appears to have been made on Friday without an official announcement, prompting criticism from MPs.
Yasmin Qureshi, Labour MP for Bolton South East and shadow international development minister, said: "I was not informed of this and I understand nor was anyone else in Bolton.
"I'm just gobsmacked. They're making such an important announcement and they don't even have the decency to tell us or tell our constituents.
"This is typical of this Government's incompetence."
Layla Moran, chairwoman of the All Party Parliamentary Group on Coronavirus, said updating the guidance without a proper announcement "is a recipe for confusion and uncertainty".
The Liverpool Echo sends newsletters on a wide range of topics – including our daily news bulletin, now going out three times a day.
There are others on what's on, politics, court news, Knowsley, Wirral, and arts & culture, as well as both Liverpool FC and Everton FC.
Signing up is free and it only takes a minute for you to get the biggest stories, sent straight to your inbox.
How to sign up for an Echo Email Update
1) Go to our dedicated newsletter page at this link.
2) Put your email in the box where indicated
3) Tick as many boxes as you like, for each newsletter you want.
4) Press Save changes and that's it!
She said: "Local people and public health leaders in these areas need urgent clarity from the Government. Matt Hancock must come before Parliament and make a public statement to explain these new rules."
Newly elected West Yorkshire mayor Tracy Brabin added the change could cause "anxiety and confusion".
Ms Brabin said she would raise the matter urgently with vaccines minister Nadhim Zahawi on Tuesday.
She tweeted: "If Govt are concerned we need clear guidance and support not advice that could cause anxiety and confusion."
Meanwhile, quarantine requirements will reportedly be maintained for those who come into contact with positive cases after June 21 even if they have received both doses of the vaccine.
The Daily Telegraph said this could mean the nearly 23 million people who have had both doses could be forced to isolate for 10 days if contacted by the NHS, adding a negative test would not allow an early end to quarantine.
Separately, the Government will be facing an urgent question from Labour's shadow health secretary Jonathan Ashworth on Covid-19 on Tuesday.
A Government spokesman said: "Working with local authorities, we took swift and decisive action to slow the spread of the B1.617.2 (India) variant by introducing surge testing and bringing forward second doses of the vaccine for the most vulnerable.
"We provided additional guidance for those living in affected areas when we became aware of the risk posed by the variant, to encourage people to take an extra cautious approach when meeting others or travelling."