I am on a 3 months rent contract that started 31/12/2020. On

I am on a 3 months rent contract that started 31/12/2020. On 05/02/2021 the Agency gave me notice to move out in 55 days. I said to the Agency that now during the pandemic they must give 6 months notice this is the new Government Rules. I found another place but I want to move before my contract ends because the Landlord doesn’t wanna give us 6 months notice, and the Agency says I need to stay until the end of my contract. Is it ok to move before my contract ends and can I ask my deposit back?
JA: Where are you? It matters because laws vary by location.
Customer: England
JA: What steps have you taken so far?
Customer: I’ve just sent emails to my Agency asking if they want us to be flexible and understand the Landlord doesn’t wanna give us 6 months notice, they should be flexible as well and allow us to move before our contract ends as we found a good place already that fits in our budget.
JA: Anything else you want the Lawyer to know before I connect you?
Customer: No