It's an interesting question in the context of what I suspect is an increasingly common scenario.
First off, the fact that your tenant now lives with his partner and child does not of itself either terminate the existing tenancy or create a new tenancy. Your tenant's partner has no rights relating to the apartment and, equally, owes you no contractual duties (eg. to pay you rent, etc.). Your contractual relationship remains exclusively with your tenant.
The fact that your tenant shares possession of the apartment with his partner and child does not of itself constitute sub-letting. The relationship between a head-tenant and sub-tenant is akin to the relationship between a landlord and tenant (i.e. the head-tenant would be entitled to rent from the sub-tenant, etc.) and there are particular statutory provisions around sub-letting. I assume that's not the case here.
It is possible that your tenant is in breach of his letting agreement with you. It is quite common (but certainly not always the case) for letting agreements to provide that the property may only be used as a private residence for the exclusive use of the tenant and to expressly prohibit the tenant from sharing possession of the property with anybody else.
If that's the case here, then you would have grounds to issue a lawful notice of termination of the tenancy. You would then be in a position to try to negotiate a new arrangement with what would become your joint tenants if you choose (although you would still be subject to the RPZ regime).
That's the legal position as I see it.
As a practical matter, if I was in your shoes, I would just accept the status quo and review the rent in October as per the RPZ formula (don't forget that you have to give 90 days' notice of any increase to the rent).
As an aside, I happen to think that the RPZ regime is grossly unfair and counter-productive in terms of achieving its stated objectives. One of the truly objectionable aspects of the regime, IMO, is that it sets landlords and tenants at loggerheads with each other instead of encouraging them to negotiate their arrangements like adults. Rant over.:mad: