Do English pubs still have several different bars?

Some still do - but it is the exception rather than the rule. For various reasons - not least staff costs - pubs have now tended to merge their bars so that the need for separate staff for each bar is eliminated or reduced. Another reason is simply that we have all become more egalitarian and the traditional distinction between "white collar" and "blue collar" workers has almost gone.

When I started drinking, fifty-five years ago, it was not usual for pubs to have up to five different bars: The public (where the beer was cheapest and the workers drank); the private (more expensive where the better off - office staff and their ilk) would drink; the lounge (even more luxurious, where the bosses drank) and the private (where those who could afford it would entertain someone else's wife). Of course, the drinkers would all be men; unacompained women didn't go into pubs unless they were "working girls". There was just one more bar - the Bottle and Jug. This was a small serving area, with a separate entrance, where people could buy off-sales drinks. Although anyone could use the Bottle and Jug, it was commonly used by wonem who wanted a bottle of port or similar to take home - but who would never have gone into the bar areas which were, as I have said, full of men.

Some pubs did have cocktail bars - but these were more likely to be found in hotels.

Many local traditional british pubs still have a bar area and 'lounge' in separate areas, most don't have private areas and none have cocktail bars- this would be more likely to be found in a hotel. 50 years ago, UK pubs didn't have cocktail bars. You would be lucky to get a slice of lemon in your gin and tonic! 50 years ago a Babycham or Snowball was considered exotic in a pub.

If you want to be authentic, you need to decide on what decade your story is set, what kind of area ( working class, posh) and the characters. Might be best to decide what part of the UK, and then the neighbourhood within the area, your story is set in, as pubs differ quite a bit in terms of drinks served, atmosphere, types of people that frequent etc.Many UK pubs derive their name from historical roots, and this might be interesting for a story.

This is my local pub, it's a good example of a typical british pub these days.

yes all the local ones to me still do as they hold meetings such as rotary meetings in some of them. Also another angle you could add are the beer gardens etc

http://en.wikipedia.org/wiki/Public_house

http://en.wikipedia.org/wiki/Western_saloon

http://en.wikipedia.org/wiki/Bar_(establishment)

These sites may help you.