They are self imposing the rule BUT you do have to get the lender’s consent otherwise the tenancy is illegal and there will be a provision in the lease not to do anything which is illegal.
Depending on the terms of the lease allowing you to sublet, it may be that consent cannot be unreasonably withheld or delayed in which case, you could argue this is unreasonable but it’s more likely that you cannot let without the landlord’s consent and no more, and if that’s the case, they are at liberty to impose whatever terms they like including sight of this permission.
They can usually also charge you for the consent but only if it says so in the lease.
Can I clarify anything else for you?
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