We have not signed any contract and I was still mulling over whether to accept what I saw as a very poor offer.
English law enforces verbal or oral contracts though they are harder to prove.
You have not signed such a document. However there may be an oral agreement to assign which the local company could enforce through a court order. First you need to determine what intellectual property rights are relevant however. If it isdesign rights then if the local firm commissioned the rights they will belong to thecommissioner, though this is not the case with patents and copyright unless agreed in writing. Whatever the rights if you agreed to do these designs for payment by that firm you have almost certainly granted them a licence to use even if no assignment was agreed.