Do part-time employees need to give notice?

I have worked for the same company for nearly nine years and since returning from MAT leave I have worked part time. They have been difficult employers and during one of my battles with them I was verbally reminded that I did not in fact have a contract at all. On returning from MAT leave I was never given a new contract reflecting my part-time status or a letter outlining my new working hours and new pro rata salary. To be honest it never crossed my mind. Now finally a fantastic job opportunity has arisen. So, two questions. As I don’t have a contract how much notice do I give? Now to add to this my boss is really quite vindictive – he would think nothing of giving me a bad reference or refusing to give a reference at all. What is the legal requirement around references?