Even though the tenant has not been provided with a written contract, she has a shorthold tenancy on the property and the corresponding level of legal protection. (By not providing a written contract the landlord might leave himself in a worse position, if any dispute arose, than if he had done so).
If the landlord collects the rent weekly, he is legally obliged to provide a rent book. Otherwise (oddly) he's not.
There is no legal obligation on the landlord to provide a receipt for rental payments (unless a rent book is required by law, as above) but the tenant would be well advised to offer a simple form for him to sign each time he calls to collect the rent. (i.e. she could effectively produce her own rent book).
This pdf confirms my statement about rent books and provides additional information about shorthold tenancies:
http://www.communities.gov.uk/pub/919/Assureda ndassuredshortholdtenanciesAguidefortenants_id 1151919.pdf
Chris
(PS: I still support your suggestion of consulting the local CAB)