Hi and welcome to the forum djog/Rjmac.
Absolutely right Rjmac - you can leave property with 28 days notice at any point. The only way the tenant notice period can be amended is AFTER the tenancy agreement is signed and you cannot be coerced into this - only if you agree to change the notice period.
Deposit should be registered with a deposit scheme within 30 working days of start date. Once tenancy ended, either by you or landlord giving correct notice - the deposit is released by the scheme.
There is also a new code of practice (set of written rules) for letting agents to follow which by the sounds of it would be pertinent to both your situations.
Have you been dealing with the agency in writing so far Rjmac? Be interesting to look at the"pro-forma" they gave you djog - not sure how this would comply with the new code?