Please help question about child's nursery

[PrincessII]

We never signed a contract with my child's nursery. There normal notice period is a term.

As we haven't signed a contract and my we have had problems with the care given, we have given them one months notice.

My child has only been their since sept and I presume that if there is no signed contract then I could technically just walk as long as fees are paid.
I felt one months notice is adequate and all fees will be paid.

I my presumptions correct? Any help would be appreciated.

I think that as you knew their terms when you started you are bound by them, whether you signed a contract or not. This is seperate to the question of whether they have been in breach of contract.