The tenancy agreement is a contract, so you have a contractual obligation to abide by it. It is a contract with tjhe landlord - not the letting agent - so the landlord may be entirely unconcerned if the restrictive clause has been put in by the agents. You could ask the landlord & find out.
I'm not sure what would happen if you just ignore the clause & go to a different supplier. I suspect you could be sued for breach of contract & be made to pay the Court costs & whatever loss the landlord has incurred by your breach.