What is the best way to imitate a London accent?

You would have to define a London accent, there are many.
Not everyone in London is born within the sound of Bow Bells.

Which one? There are a few.

I was born in London and many have Tried and Most fail Leave it to us experts

You Can Not there is only one true Cockney accent

Estuary is NOT a London accent but a southern England accent

Not Born in London you will always get it wrong

watch the Idiot that Ruined Mary Poppins

it was not even English Let alone London Cockney


It aint my fault yous dont talk propper like what i does

and i wet myself Laughing when some yank try the Australian Gday

For a good imitation, you will need a dialect coach.  I used to work in theatre in the UK and in one play, there were British and Irish actors both learning a Canadian accent.  Both were given different techniques depending on where they came from as both used their mouths differently to begin with.
If you are doing it for fun, then just find some videos on youtube. There are plenty on there giving you the subtleties of accents.

Cockney's (don't pronounce H) Cockney alphabet starts with A for Horses (Hay)