What are my rights?

I've worked in a hotel for 3 years now (since it was opened) and i've been very loyal.

I'm on a 0 hour contract there, which i believe if they offer me work and i can't do it, i'm not breaking any contract and the employer understands this.

However last night at work they said to me, I 'HAVE' to work one of the following -Boxing day or new years eve. Boxing day is my birthday, of which i always spend it with family for a nice meal out, and new years eve i always spend with family always...

These are important for me as throughout the year, i don't get to see much of my family as they live in different counties/countries, however work don't seem to care about that...

Will I have to work it if they give it to me? :/