Management charges UK

Is it normal for a letting agent to impose their management charge on repairs carried out?

E.g.
Letting company charges management fee of 10% deducted from rent monthly.

Smoke alarms need to be fitted cost £117.50. Invoice from third party reads £100 + 17.5% VAT.

Invoice to landlord £100(net of vat) + 10% + Vat(17.5) = £ 129.25.

Not as far as I know - but check you agreement with the letting agency - what does that say?

Nothing in the letting agreement.

Just wondering if any other UK property owners experienced something similar.

The obvious flaw is that it if choosing between two contractors to do a job it would be in their interest to choose the more expensive one.