Change from Managed Agency to Self ... ref: deposit

Tenancy Deposits

In January I spoke with the Tenant and they confirmed their intention to stay for at least another 2 yrs and confirmed my suspicions that the agency were doing nothing... difficult to contact, slow to respond etc., although they are reputable and we feel good about them.

Anyway, we decided to stop using the agency and do this ourselves, and the tenant agreed ... The tenant is renting their smaller home out, so are in a similar position to us (they want a good tenant and so do we, kind of thing).

The agency refuses to refund the deposit to the tenant, saying that it should be protected. They also mentioned I (the landord) dont have a scheme where I can protect it, so they (the old agency) should keep it for them.

<snip from tenant email to me>
She told me that it is a statutory requirement that tenant’s deposits are held in a registered scheme, so to release the deposit to you if you are going to continue renting the property, they must first check if you are have such a scheme. It is possible, she told me, for an individual landlord to have a scheme, but she indicated that it wasn’t worth it.
<snip from tenant email to me>

Questions:
- Does this sound right? I have no problem with the agency keeping the deposit, so long as they release it upon termination of contract.
- Do I need a contract with the agency too, for this to continue?
- Would they be able to split the deposit at the end, if some is needed to be withheld etc.
- I joined RLA as I was told there is a Deposit Protection Service I can use on here, but that seems to be done elsewhere, not here. When I click on the link it takes me to a new website (Computershare), do I need to join them too?

Thanks in advance for your help.