Experience in England

I'm planning to have one-month experience in England, probably in London, between next November and December and I need some suggestions or help...please.

I know that probably these are not the best months of the year for staying in England but, with my job, I have to go in November.

 

I'm thinking to stay in London because is a very large city and my goal is to have a real full-immersion in the british's coulture and also go deeper in using English language with native speakers (without attending any English course) and also enjoying my holidays. I already stayed two times in London, in the past years, only for few days and I really like it.

 

I'm considery to stay in the zone 3 or 4 more or less in a shared room or b&b and I'm searching for a very cheeper accomodation.

 

So my question are:

 

- Witch is, for you, the best accomodation I can choose? Do you know any alternative form of  accomodations that will be ok for me?

- Zone 3 or 4 are ok?

- Do you have any other suggestion or advice to give me?

 

thank you