Hi Victoria,
Below is info that officially compares Oyster cards with the paper alternative 'Visitors Travel Card'. We just used a pair of the latter (i.e. one week per each card) without any trouble.
I am done. The end.
'The Visitor Oyster card is a contactless smartcard that carries credit which you can use to pay for journeys on all public transport on the Transport for London (TfL) network. It is valid in all travel zones and automatically calculates the cheapest total fare for all the journeys you make in a single day.
The Travelcard is a paper London travel pass which is valid for either a single day or seven days, and is available for certain combinations of travel zones (Travelcards for consecutive days will be posted as single day cards for each day of travel. For example, 2 x 3 day cards will mean you will recieve 6 cards in total). It is also valid on all public transport on the TfL network.
Whether you should get the Travelcard or Oyster card depends on how long you’re staying in London and how frequently you’ll be using public transport.
If you are in London for a week and plan to use only the central London Travelcard zones on a daily basis then a 7 day Travelcard might be the most cost-effective option. If you plan to stay in London for a shorter time or want to travel to the outskirts of the city, the pay-as-you-go Oyster card cost might be cheaper.
For more detailed advice on which travel pass is right for you, please visit our read our guide to London transport tickets.'