Update previous post
Update: I handed the keys back today and the letting agent has finally confirmed that my notice ended the tenancy for both tenants. They advised that if the remaining tenant wishes to stay, they will need to take on the full rent under a new arrangement.
However, the agent is now saying they cannot return my share of the deposit yet because they consider the tenancy/contract not to be fully concluded.
Thank you to everyone who gave advice and shared their knowledge — it has been very helpful.
My next question is: if the tenancy has ended for both of us, can the agent legally continue to hold the deposit, and what would be the best way to recover my share? Any advice would be appreciated.