Seems to be like some are looking at this with blinkers on.
From a 'consumer' point of view Alice is well within her rights to question everything she has had to take from that letting agency.
And the fact that she has actually asked other local agents in the area on a rolling contract seems to have been missed by others. After an initial term a contract should proceed on a rolling basis, that's standard as outlined
here"An assured shorthold tenancy gives people a legal right to live in their home, either for a fixed-duration or on a rolling contract known as a periodic tenancy."
"Tenants on fixed-terms can only end the tenancy during that time if their agreement says so, dependent upon the agreed notice period. From the date the fixed-term ends a tenant can leave, but should still give a month's notice to the landlord. If the tenant opts not to leave, the tenancy becomes a rolling agreement. Tenants on periodic tenancies or rolling agreements should give one month's notice in writing, ending on the day rent is due."
The one problem you face Alice is that you actually signed it. I know you were given little choice but fighting it retrospectively is going to be difficult. The fact that you knew what you were signing and still signed it will be difficult to argue against. In hindsight it would have been better to fight that issue at the time.
Perhaps it would be wise to focus on one battle. What's more important, the contract or not getting ripped off? I would guess the money. You want to get out of there with as much intact as possible. Maybe forget the battle on contract notice based on the difficulty of winning it and focus on getting your money?
At the end of the day you want to just get out of that agency full stop and get as much of your deposit back as possible.