Steve, have a look at Meguiars . I've used their clay bar in the past and you need to use lubrication with it, such as Meguiars Quick Detailer. It will gently take off surface contaminants and any traces of wax as well, so you need to reseal the surface with wax afterwards.
This.
Just back from the butchers.
Buy yourself a clay bar and matching lubricating spray. Don't be a cheapskate and use washing up liquid. Buy the proper stuff.
Wash and dry your car in the normal way.
Pull off a 50p sized dollop of the the clay.
Spray maybe a one foot square area of paint work with the lubricant - I'd do this when the car is cool and not in direct heat such as we've had recently.... So, spray the area and then GENTLY rub backwards and forwards (not circular) over the lubricated area.
Once your panels have been clayed, as Jays says, they are then unprotected - naked, vulnerable! You will need to wax these areas to protect them.
You will not damage your paintwork.
Take a look at the clay surface that you've been rubbing with. It will be black with crap from the paintwork. Fold this in to your blob of clay, spray a new area and start again.
Once clayed, your paintwork will feel super smooth to the touch and all marks removed.
Far better to use this somewhat laborious technique than any cutting polish or compound.
