Yes, if I recall my distant stint as as consultant, I believe you can only claim back if you're genuinely mostly self-employed and the equipment is to support that. If you are employed, then it's your employer should be buying the necessary equipment.
Expenses are different, that's a payment to cover any additional expenditure, but I don't think you should be claiming double on anything (as the employer will also be offsetting their spend in much the same way).
Accountants will know better, I got sleepy just writing this.