Nursery Debt - Am I Liable?

Hi all, 

New here, I hope this is the right place to post and that someone has some advice or even just some clarification on the matter!

My daughters joined their nursery provider in February 2019. Both my ex-partner and my name & signature are on the application pack/contract, within the application pack it says we are both responsible for paying nursery fees. 

I made full, regular payments each month between February and July 2019 to the nursery. 

I left the relationship in June 2019, I made maintenance payments (family based) to ex between June and October 2019. 

In October 2019, ex opened up a CMS case. These payments started in January 2020 (they were backdated to include months from October 2019). 

I have made full, on-time maintenance payments to date. CMS payment plan and the child arrangements order I obtained from the court are the only agreements we have in place. 

In November 2020, I received an email from the Nursery stating that the account was in debt, in the region of £16,000. I spoke to the nursery and my ex regarding the issue, my ex informed nursery to contact her regarding the issue as "she deals with the payment of nursery fees" (which she has done since separating in June 2019), she was making full, on-time payments to the nursery from the time of us separating in June 2019 until June 2020. Her comments to the nursery closed the matter for me and I did not hear anything further...

I then received further correspondence from Nursery in May 2021 stating that the debt had risen in excess of £20,000. The owner of the nursery stated that as my name is on the application form/contract for when the girls started, if they were to pursue legal proceedings it would have to be against both my ex and I. 

I advised the owner to put my children's place at nursery on hold until they had written confirmation from my ex acknowledging the debt and agreeing to a payment plan, which they carried through with. They have a written agreement between themselves (nursery and ex) acknowledging the debt, and agreeing to a payment plan to clear the debt. This agreement was made in July 2021, however since the children no longer attend the nursery, ex has stopped making payments to clear the debt. Thus, Nursery have contacted me out of courtesy to tell me to expect a letter from their legal representation to claim back the money. 

There have been changes made to the original application pack/contract that I signed in February 2019, i.e. the amount of days the children attend nursery, which have been made by my ex alone. These amendments included removing the term-time agreement we had in place (increasing the girls time spent in nursery) as well as increasing the time that the children spent in nursery during the first national lockdown (despite me being available to care for the children during this time). Both of these decision were made without my agreement or consent. I explicitly made my ex aware that I strongly disagreed with the children attending nursery during lockdown at the time, however, she made the decision to have them attend full time, they were the only children to increase their time spent at the nursery during lockdown. 

Alongside this, during our court case, ex/her solicitor put forward that "Ex pays for the children to attend nursery full time, the cost of which is bourn by her alone" - a clear acknowledgement that she is fully aware that she is responsible for nursery fees.

Ex has also made me aware of the fact that she is claiming benefits via universal credit for childcare - I'm under the impression that the total cost of childcare that she pays per month is taking into account when making the calculation for the contribution she gets? - Surely if this isn't being used for it's sole purpose there is an element of sharp practice?   

My question is, am I liable despite the above? I received no correspondence from my ex or the Nursery regarding the debt until it had reached £16,000 (despite them having my full contact details and address). When I was made aware of this debt, I was excluded from further correspondence due to ex stating she is responsible for all fees with the nursery. Nursery has a written formal agreement from Ex acknowledging the debt and agreeing to a payment plan. The terms of the original 'contract' signed have been changed/amended numerous times without my agreement or consent. There is a CMS payment plan in place which I adhere to. Ex has more than likely been claiming help towards childcare from gov/benefits. Numerous correspondence from ex stating that she is responsible for Nursery fees. 

Any confirmation, clarification or advice on the matter would be much appreciated. 

Thanks