In colloquial British English, the 'Good' is often dropped from greetings.
e.g..
'Morning (Good morning)
'Evening (Good evening)
guv'nor
short for 'governor' which means 'boss'. A term of respect for a customer (who is the temporary boss). Often shortened further to 'guv'.
Usually 'a while' means a short period of time. However, in this case the taxi driver means that the trip will take longer than expected. An example of British 'understatement'.
Short for 'Look here'. In colloquial British English (in this case the Cockney dialect of London) this expression is often used to introduce a new topic.
Never been further than Calais--and that was a day trip!
In using this sentence the taxi driver indicates that he is not interested in countries outside the UK. Calais is the closest foreign port to the UK. This is like a Japanese saying s/he has never been further than Pusan (on a day trip).
Short for "I will tell you what--". A way of introducing a new topic or adding further information. In this case the taxi driver does not want to talk about France, so he changes the subject.
I had that (famous person) in the back of the car once.
London taxi drivers like to tell stories about famous people they have carried--and about their behaviour. In this case he was quite impressed with Ms. Sugiyama.
In colloquial English, word order is often reversed. In standard English this would be "She was a nice girl".
London taxi-drivers often consider the tip to be compulsory--possibly as a charge for their entertaining conversation. About 10-15% of the fare is a reasonable tip.
A way of saying 'Thank you' in cultures where Christianity is the dominant religion.
Mind the step now.
Mind (something) is a way of saying 'be careful' (of something). The London taxi has a ground clearance higher than normal cars.
e.g.
Mind your head (sign over a low doorway).