I do not understand exactly what is happening here.
If I have guessed correctly, they must give you notice to leave, and that is currently about six months.
If they want to return the deposit and you have already moved in, then they cannot make deductions without explaining why, and you agreeing that it is reasonable.
I believe you cannot have the deposit back until you have applied to the deposit holding company. Your deposit should be held by a third-party and you should’ve been notified of who is holding that money.
The certificates should have been supplied before you moved in, and the contact details of the deposit holding company should have been provided.
Do not provide bank details until you know that the agent and the landlord are legitimate. One check is the fact that your deposit should be held with a Tenancy Deposit Scheme holding company*. I believe you can check their websites to see if it is held - there are only 3 companies like this for each UK country. If none do, then the deposit has not been registered. If you have been given the keys, the deposit should have been placed with one of them within 30 days of giving it to the landlord or agent.
Do not rush into anything. Do not agree to anything until you have had more advice.
Take one step at a time. Look out for the advice from others, I am sure, below.
Tell us what your situation is: have you moved in, or not?
If you have moved in, has your agreed period of stay, called a term, typically six months, ended or not?
What do you mean by a deposit: a small amount to reserve the place, or the full amount of up to five weeks of rent?
Good luck. I rarely visit this site, so it is by chance I am here.