Notice period after TUPE transfer

BurnCK

I was TUPE transferred to a new company last week but am wondering whether my notice period from my previous company will apply? It was previously 3 months (negotiable). 
I feel that 3 months is way too long as it's hard to find jobs where the employer is willing to wait that long, especially for a mid-level position such as mine. I understand I could just refuse to work the full 3 months and I know there would be no financial loss to my new company and the only thing I would have to consider is a reference, but as I have barely worked for them I wouldn't put them on my CV anyway. However, as part of my TUPE transfer I am still working at my previous employer, at least until our jobs likely are moved offshore next year. I suppose my question is, could me not working full notice period affect my reference from my old employer, as I'm not actually employed by them now?

TELLIT01

I was under the impression that all employment rights from the original employer remain following TUPE.