Whether you wish to rent or buy in London, it is advisable to prospect well in advance of your arrival through real estate agencies that advertise online.
There are publications in French that advertise housing, jobs and employment classifieds. Ici Londres and Bonjour London are a real goldmine for French people who settle down! The daily newspaper Loot will also be useful. Also think about the Centre Charles Péguy, a French association that helps young French people arriving in London.
For temporary accommodation, think about "Bed & Breakfast", those rooms that are rented in private homes.
You should also be aware that "flatsharing" is very widespread in Great Britain. So, if sharing an apartment or even a house with several people is a solution that suits you, don't hesitate! You just have to know how to take advantage of the advantages and disadvantages of this way of life: lack of intimacy, peace and quiet, impromptu departure of one of the roommates against a larger living space, a divided rent, the same for the bills...
Note that such an option can be an alternative to the loneliness one can feel when moving to a country one doesn't know well.
Once you've found your cozy nest, you can apply for housing assistance from the Local Council (the equivalent of the town hall) that you depend on. There are currently two such councils. The first is called the Housing Benefit, which is a housing benefit for a set period of time. The Council Tax Benefit is the full or partial payment of your Council Tax.