The landlord is able to remedy the issues ‘within a reasonable time’ however there is an implied term in tenancies that the property must be fit for human habitation the day of letting.
A new law was brought into force in 2019 that means properties must be safe, healthy and free from things that could cause serious harm.
Whilst they may argue the cracked window may not be a hazard, you can argue that the property is not fit for human habitation the day you attempted to move in due to its condition.
The cracked window is likely to cause a draft, rain water to get in and cause dampness and mould which can also be detrimental to your health. Depending on how long the crack has been there, there may already be damp in the property. One of the main factors of determining whether the property is fit is ‘freedom from damp.’
Another factor is sanitary conditions which the property does not appear have.
Another factor is sufficient ventilation – if you are unable to open the window properly, how are you able to ventilate?
Another factor are hazards under the Housing Health and Safety Rating System. The prescribed hazards include hygrothermal conditions – damp and mould growth and excess cold (given the crack in the window these are definite possibilities).
I would argue that on the above factors, the property is not fit for human habitation and due to this, you require your tenancy agreement to be ended and full deposit and first month’s rent returned to you.
Sorry this is a bit long winded but I hope it helps?