A member of the team I work in is permitted to work from home one day a week (this was a reluctant agreement as the individual had been offered another job and would leave unless granted the one day from home) We are the same level, same job role. I have recently put in the same request and have been refused for the reason that if 'its granted to me then the remainder of the team will want it'. I have had an excellent annual review, my reasonings for wanting to do it are the same as my colleagues (more time with children). Is this allowed or should there be consistency?

The employer basically makes the rules unless the employees are by contract or have a union.

As long as employment is at will (you can be terminated for something or nothing) an employer can favor one employee over another.