Variation of part-time hours
A. Almost certainly not. Contracts can only be changed by agreement. Your employer is suggesting that this contract term permits them to change your contract unilaterally, that’s to say, without your consent.
Courts and tribunals generally take a very restrictive approach to interpreting this kind of term. In particular, the law only allows employers to make unilateral changes where the language in the employment contract is clear and unambiguous. This particular term does not give your employer the clear right to change your hours without your agreement.
There are other legal arguments you can make to resist this kind of unilateral change. Have a look at a useful new ruling from the Employment Appeal Tribunal — Hart v St Mary’s School (Colchester) Limited [2015] UKEAT/0205/14/DM which involved an unsuccessful attempt by a school to force a part-time teacher to change her hours.