I presume you haven't got your P45 yet so. Tell them that you need your P45 urgently and they will have to sort out final payments to prepare it. If they won't give it to you try ringing the tax office to say you haven't rec'd a P45 from your previous employer. I have seen cases where a helpful officer will contact the previous employer to chase up the P45. Might put the skids on.
Contact the DETE Employment Rights section who should be able to apprise you of your statutory rights in this situation. They are very helpful in my experience.
Better to put stuff like this in writing (i.e. a letter rather than an email) to make it more formal and to keep a paper trail just in case things get contentious.
Just for the side of the employers, it is end of quarter, so maybe his excuse is valid. Im not saying this shouldnt have been sorted sooner just saying the busy week and auditors thing does make sense.