The British- and Irish-English expression duvet day denotes an unscheduled extra day’s leave from work, taken to alleviate stress or pressure and sanctioned by one’s employer.
—Australian-English synonym: doona day.

The earliest occurrences of the expression duvet day that I have found are as follows—the first wo seem to indicate that, in Britain, the practice was initiated by Text 100, a London PR agency:

1-: From the Financial Times (London, England) of Monday 30^th September 1996—as quoted by the English Oxford Dictionary (online edition – December 2020):

There are days when one’s mood is so sour that the only solution seems to be to stay in bed. […] Staff at Text 100 […] can take a ‘duvet day’. Each employee is allowed two days a year when they can play hookey with their employer’s blessing.

2-: From The Mirror (London, England) of Thursday 9^th July 1998:

DUVET DAYS

At London PR agency Text 100, they’ve got the perfect solution for those days when “you just don’t feel up to it”.
Staff can ring in and claim a Duvet Day—simply an unscheduled holiday. Each person is allowed two such days a year. These can be taken at any time, provided no serious disruption would be caused.
“People love them,” says marketing manager Mark Pinsent. “Knowing they’re there is a great boost.”

3-: From Every office needs… a slacker who takes “sickies”, by Damon Syson, published in the Evening Standard (London, England) of Monday 20^th November 2000:

Every office needs a slacker. Being lazy and late, taking the odd unofficial “duvet day” (especially when you’ve just started a new relationship), spending longer at lunch than everyone else—these are all vital stitches in the rich tapestry of office life. You’re like the person at school who always comes bottom in maths tests. While the other kids are stressing through their exams, they have the reassurance of knowing they could never score as low as you. You are therefore performing a valuable service.

4-: From The next time you feel sick—take a duvet day off work, by Mark Solomons, published in the Evening Standard (London, England) of Tuesday 2^nd January 2001:

The creeping nausea and quiet guilt of nursing a New Year hangover at work could be finished forever if British businesses adopt a practice from America that allows workers to take a day off at short notice.
The introduction of “duvet days” in America has rendered the tradition of “throwing a sickie” redundant by allowing workers who have over-indulged the night before to call their workplace in the morning and legitimately take the day off.
The system, which gives workers up to four duvet days a year, was devised by managers in America who were tired of staff offering lame excuses or getting their partners to ring in for them after waking up with a hangover. Duvet days are built into the annual holiday entitlement, guaranteeing companies that workers will not get any more holiday then they would previously have enjoyed over the year.
Workers continue to think of the days as a bonus because they do not have to be booked up weeks in advance, and find them more useful than a day off taken simply to make up the allotted holiday entitlement.
The idea follows the introduction of dress-down Fridays, designer coffee shops and water coolers as the latest office innovation to cross the Atlantic.
Sarah Parsons, head of communications at recruitment company Reed, says that Britain’s skill shortage makes duvet days an ideal addition to benefits packages to attract the right staff.
“Alongside better health and pension benefits, companies now offer employees increased holiday entitlement, gym membership and even subscriptions to dating services,” she said.
“Duvet days are the latest in a list of ‘employee-focused’ benefits.”
But she warns: “While the idea sounds great, in reality individuals should be wary of abusing it. Just because you’re feeling lousy that day doesn’t mean that someone else will carry your workload—it will still be there when you get back to your desk.
“Duvet days may not be appropriate for some types of staff, or indeed organisations.
“But, in practice, employers who use such benefits tend to engender a loyal and dedicated workforce—it appears to be a case of ‘you scratch my back and I’ll scratch yours’.”
Up until a year ago, dress-down Fridays were thought of as a purely American practice but have since become common now all over Britain.
Women’s magazine Company has predicted duvet days will prove popular in Britain.
“Sometimes, you just can’t face struggling in to work. You’re not ill at all, but days like this are meant for throwing sickies,” Company says.
“But if your boss isn’t quite that enlightened, you have no choice but to tell a little white lie so you can stay in bed for the day.”
The magazine suggests getting a partner to take the same duvet days as well, to have breakfast and sparkling wine in bed and watch Richard and Judy. *

* This refers to Richard Madeley (born 1956) and Judy Finnigan (born 1948), a British married couple who were then the presenters of This Morning, a television programme broadcast on ITV.