How does the dental care system work ? (London)

Hi,

I've recently moved to the UK and want get my teeth checked and full dental hygiene service done. Can anyone tell me how the dental care system works in the UK?

I'm a bit uncertain about things like: Do I go to NHS dentist or is it better to chose a private dentist? Is this dental hygiene and check-up usually done at the same place or different services? Is it self funded or covered by NHS if you go to NHS dentist? etc.

General advice and possibly concrete dentist recommendations in East London (around E1) would be highly appreciated.

Thank you !