Jen I think thats one year rather than two you're referring to.
But regardless, you can still be unfairly or unlawfully dismissed in your first years service.
Unlawfully if you have been discriminated against in grounds of: age, race/ethnicity, sex, marital status, sexual orientation, disability or religion.
Unfairly if you have been whistleblowing, on jury service, lots of reasons including challenging your employer over some basic employment rights such as H&S
Talk to your citizens advice next week where you can explain the details of your particular circumstance.