It is many moons since I did my Employment Law course, but found this on line.
An employer has defence for discrimination if he can demonstrate the following:
The treatment is to achieve a legitimate objective, such as a genuine business or operational need
The treatment is necessary to achieve that objective and is
A proportionate way to achieve that objective
In this case a part timer would probably not have been able to meet the business operational need if they would be required to be in the office outside their normal hours.
As there are 4 other long serving F/T she probably thought you were the best person for the job, and sent off an Email without thinking carefully enough about her wording.