There is not straight 'yes' or 'no' answer to this one.
If it has been made a specific condition of employment, then that's pretty clear - but you say it isn't.
For customer-facing departments (like reception) it is possible to demand minimum standards or even specific dress-codes.
Of the various potentially 'fair' legal reasons for dismissal, this one would potentially fall into 'misconduct'. It would be a brave employer that decided to dismiss for reasons of dress in jeans. The test, of course, is that employer would have to dismiss, then the employee would have to challenge the dismissal through an Employment Tribunal.
You are therefore probably on safe grounds, but don't expect 'the management' to appreciate your stance. There are various ways to put pressure on an employee.