Yes, but often no!
If seven day working is the norm, and a requirement of the job, then it would be safe to assume you can insist an employee works on Christmas Day (and/or Boxing Day). In other circumstances you would need something specific in the contract to support a requirement to work on that day. If “push comes to shove” it is not sufficient for there to be a mere expectation that someone will work on that day – for example because they have failed to meet a deadline. There needs to be some clear term implied (eg it is the working norm) or explicit (in a written document) if you are going to insist that en employee works on that day.
Legal rights apart it is important to consider fairness. Uneven distribution of the load of working Christmas Day (eg the same person gets that day off year after year) may seriously affect the commitment and motivation of staff. Additionally most employers give a premium eg time and a half or even double time for working Christmas Day. Employees are also, of course, entitled to the day off at another time.
Happy Christmas all round!