Tenants owe £10k but daughter is asking for a good reference?

Yes, that's a good starting point. You may not get all of thats owed but be prepared to negotiate.

However if your reference is dishonest or even negligent then you could theoretically be on the hook with her new landlord. Unlikely the new landlord would take action, but it's theoretically possible.

I’d just say no. As you say, she isn’t your tenant.

As already mentioned. you seem to have had no transactions or dealings with the daughter. and You therefore are not in a positron to giver her a reference.... Nice try by the daughter.. I remember a friend who wanted an employee to leave but had no real grounds to sack her etc... So he gave her a good reference to help her move on you can guess what she did. Employment tribunal. if she was so good why were you actively trying to get her to leave. I think it was silly of him. But as he said. IT GOT her out of his hair... sometimes we have to make commercial decisions

I would point out that almost all landlords ask these questions of previous landlords when requesting references.
Are there outstanding arrears? Have the tenants paid promttly And "has their been any court action" .

Tell her you only have a choice have to answer honestly or refuse to respond if asked about the tenancy at her parents address

The daughter can of course simply tell any future Landlord asking for references she has been living with her parents - this is not a lie and she is not responsible for her parents debts nor does she have to declare them - as she has no contract with you..

You might want to keep a copy of the correspondence - the daughter is inciting you to assist her in obtaining a tenancy by misrepresentation and deception.

But what ever you do don't even think about creating a false reference and ending up on the wrong side of the law.

Any such reference could even be turned against you - "here is a letter proving we have been good tenants and paid our rent on time" and our landlord is lying about the arrears. Do everything by the book !

Imagine if someone had suffered with arrears gave them the good reference to allow them to let from yourself. Then ask yourself the question again.

I suggest you don't write a reference, unless it's a truthful one. Give the details of the arrears and the unpaid debts. If however they pay the £10k owing then you can mention that too.
If you give them a good reference, they can then use that against you when you attempt to take them to court and seek a CCJ against them. Honesty is always the best policy. Dont be blackmailed into providing a good reference just to get them out of your rental property.
PS You can mention to the court how they tried to blackmail you, too!

get them to pay the arrears on the agreement you will provide a reference when asked by the next LL. Get payment first.

When request for reference comes in you can then reply honestly she has never been a direct tenant and only as a minor on an AST previously.

You can give an accurate factual reference or none at all. The reason being that fake references are rife these days, so are fake payslips and phoney employer references. If you are found to have given a phoney reference you could carry some liability.

I definitely would not give the daughter a reference, she is not a customer of yours and you could open yourself up to some hurt in the future if you lie. The daughter has got an absolute cheek to even ask you, especially with her parents inflicting the continued pain on you.
I would section 8 their butts immediately or use a 21 if no joy there, just get them out and start again. Don't just let them stay there in the hope of them settling up the arrears (10k recovery? Almost no chance without a court order, then maybe a fiver a month). In my experience, it is almost impossible to recover rent arrears and will cause you no end of stress. I always tell the tenants to get any future landlord to phone me for a reference and then I would tell the truth, whatever it is currently, as situations change. If you put something in writing, it will not go away and can be used against you.

You are at war with these people. "Won't be able to move out" haha! The bailiff will see about that. Tell her to take a hike.