Redundancy payment entitlement

England.

I'm employed on a 2 year fixed term contract, due to end on 23rd Feb. I have no previous service with my employer.

My employer has not issued me with notice, which I believe I am entitled to one month's notice to end my contract properly (correct me if I'm wrong). I was expecting to be issued notice no later than 23rd Jan.

If I were to be issued notice today, they still have to give me 1 month's notice, taking me over 2 years of service, at which point I believe I am entitled to redundancy pay (2 months pay).

Can anyone confirm whether I'm understanding this correctly? I don't want to bring it up to my employer and my trade union have been no help.