An Usdaw spokesman said the union “welcomed the debate” generated by the petition started last month by Ian Lapworth, a baker and former DJ from Kettering.
Mr Lapworth said the Christmas holiday should be respected by retailers so that staff can have “some decent family time to relax and enjoy the festivities like everyone else.”
Writing on Change.org, Mr Lapworth said: “Most retail workers are on the go up to Christmas Eve, then back on Boxing Day. Sometimes they have no choice.
“We managed 30 and 40 years ago when shops were sometimes shut for a whole week. Let’s get back to the way it was.
“Forget making money for one day, let’s concentrate on making more memories with the ones we love.”
Among the petitions’ thousands of signatories are a large number of retail workers, many of whom left messages voicing their agreement.
An Usdaw spokesman said: “Staff in retail work very long hours in the run-up to Christmas.
“Our members tell us that they need time off to recuperate as well as to spend time with their family and friends. That is especially important when they have children for whom Christmas is such a special time.
“Usdaw is seeking the longest possible break for retail staff over the Christmas and New Year period, to provide shopworkers with a breather during this very busy time.
“Usdaw won the campaign for legislation to stop large stores from opening on Christmas Day and we are calling for small stores to follow suit and stay shut.
“We are also calling for shops to be closed on Boxing Day and New Year’s Day, as well as early closing by 4pm on Christmas Eve and New Year’s Eve.”
He added: “Usdaw is not currently campaigning for any changes in shop trading hours legislation. In fact, we have been busy defending the existing restrictions against deregulation, but we welcome the debate this petition is generating.”
A similar petition launched last year, also calling for shops to remain closed on Boxing Day, received an official response from the Government saying: “We do not believe it is for central Government to tell businesses how to run their shops or how best to serve their customers. Therefore we are not proposing to ban shops from opening on Boxing Day.”