It merges into a single unit and sounds like /begjəpɑ:dən/- we often don't say I.
There are more regional types of English in the UK and some can be very different from each other and we can have difficulties understanding some regional varieties. I am not really sure whether we talk faster than American speakers or not. One thing that you might be hearing as fast language is the way we (in all variants) run words together, adding or removing and changing sounds, so that words can sound very different from the dictionary pronunciation.
And many modern Londoners do talk very differently from old movies- language is in a state of flux and BrE is changing quite fast in many ways.