One thing you DONT do let them in for any reason, even to prove YOU are innocent. I recall that there was a law that once they have been invited in they can force entry in future for the same debt. This may have changed but play safe and DO NOT let them in at all, when/if you go to get a utility bill to show proof CLOSE your door.
This is true, to a degree, it's called gaining "peaceful entry", and as I said before can be through an open door/window (if a window is unlocked but closed, they can't open it, but can open a partly open one further) or they can be invited in by an adult (so if your child opens the door they can't come in).
Once they have been in they are allowed to use "reasonable" force to gain entry again, but if you have told them that the debt isn't yours and they don't belive you (as if they did they wouldn't be coming back) and they do break in then you are within your right to treat them as a trespasser if you are there and/or to report them to the police if you're not).
In general if there is any doubt they'll send it back to their client to check, if they go busting in and it's the wrong person, after being told it's the wrong person, they can quite easily have their bailiff certificate revoked.
Oh yes, they are allowed to break into sheds, they can also break into garages, but not if they're attached to the house. They can break into commercial property under certain circumstances and with a court order which states they can, but they can't do it if it has residential property attached. (Obviously I mean in general, the rules above still apply).
The reason they break in (after previously gaining peaceful entry) is to remove goods that they "seized" (but allowed you keep hold of but not dispose of) on their previous visit. Some bailiffs have claimed that they have "seized" goods after seeing them through a window or letterbox, writing a walking possesion order and putting it through your door. This worked well for a few years, but the High Courts overuled this and said that they couldn't have it just because they saw it through the window, that was not adequate, so if they try that one tell them to go forth and multiply.
With regards to vehicles, if the bailiff clamps a car that is not on the road not only does he need to be a registered bailiff but also to be the holder of an SIA card (which must be displayed on his person), if "someone at the office has one" or he tells you that "bailiffs don't need one" tell him that the minute he leaves you're going to cut his clamp into pieces, he'll then threaten you with the police, you tell him that without an SIA card it's an illegal clamping so go for it.
Many bailiffs are good guys doing a hard job, they know how far to push it and try to help the genuine ones, but some really are low-life bottom-feeding scum who will lie, cheat and bully people until they crack. No one, and I mean NO ONE likes to hand over their hard earned money for what we often see as "nothing" (I've seen £30 parking tickets sky-rocket into the thousands) but as long as you keep calm and play the long game it usually works out in the end.