I accepted the written offer and started start-up package negotiations
Caveat that I'm not familiar with how things work specifically in the UK so maybe there is some difference there, but from a US perspective at least, a negotiation is about getting to an offer you can accept. Your only leverage in a negotiation over a job is to say or imply "I will not accept this offer; here are things you could change in the offer that would make me accept it". From there, you might be offered what you asked for, or there might be further counter-offers or discussions leading to a mutual agreeable offer, or else one of the parties walks away.
You accepted the offer, so your negotiating is done. From the perspective of the university, you've agreed to the terms they stated. It feels odd to them that now, after having accepted this offer, you've asked for more. They may wonder how many more times in the future you will ask for something additional that they can't provide.
It seems there are some communication barriers between you and the dean/directors: when they've asked what you "need", they clearly had something different in mind than you. I can't begin to guess, so you should probably ask them to clarify.
Again, things may differ in the UK, but in the US I would interpret a position without available start-up funds to be effectively a teaching-only position, where the institution doesn't have interest (at least not the sort of interest that will separate them from their money) in your research program, but is rather hiring you primarily to teach. Alternatively, they view you as sufficiently advanced in your career that you are not in need of start-up funds as you are expected to have or obtain extramural grant funding.