The Tenant Fees Act 2019 caps the holding deposit to 1 week, and a security deposit to 5 weeks.
Holding deposits are capped at one week’s rent;
Security deposits will be capped at five weeks’ rent where the annual rent is less than £50,000 and six weeks’ rent where the annual rent is £50,000 or more.
What your estate agent is saying is that your deposit would not be returned until the statutory periodic contract is terminated, as is the usual case with deposits.
In order to circumnavigate this, they have offered to terminate the current contract, and replace it with a contractual periodic, which allows the deposit to be released.
Unfortunately, for writing a new contract, they have charged you their usual fee of £90.
is the guidance notes for the Act, and on page 5, item 7 is:
The Act requires agents and landlords to refund the holding deposit except in circumstances where the tenant withdraws, fails a right-to-rent check or fails to take all reasonable steps to enter into the tenancy when the landlord or agent has done so. The agent or landlord may also retain the holding deposit if the tenant provides false or misleading information and the landlord is reasonably entitled to take into account that false or misleading information or the tenant’s behaviour in providing it in deciding whether to grant the tenancy because this materially affects their suitability to rent the property.
which hints that what your estate agent has done is illegal, but only refers to holding deposits, and you imply in your question that you have a security deposit.