Try RBK's suggestion. Remember to tune to M mode and keep the exposure constant. If one is darker than the other, you can can only conclude that the UV filter allows less light to pass through the lens, but not that the filter caused your image to be underexposed. In my own experience, I have found some filters to do that too, but usually just 1/3 of a stop or thereabouts. Whether an image is underexposed or not lies with how you set the exposure, nothing to do with the filter.
Nope. If the lens/filter let in less light, the metering will compensate to achieve optimal exposure by increasing the apperture or reducing the shutter speed. UV filter should not affect the metering.
I notice that for all my photos when viewed on my PC, they are under exposed by a bit and I have to auto adjust the brightness of the photos. Is this caused by UV filters?
i re-looked at your initial question, are you referring to the difference between viewing on your camera's lcd vs your pc? you can only do a valid comparison on a calibrated screen.