More than 55 million people will remain banned from meeting other households indoors after 2 December.
Andy Burnham said, if Covid rates continue to fall, he will push for Greater Manchester to go into tier 2.
Dan Rosenfield's appointment comes after a period of upheaval in Downing Street.
Government guidance says the bubbles should contain a maximum of eight people over the age of 11.
But in Scotland infection rates appear to be rising, according to Office for National Statistics data.