Actually, I think I'll skip it is that phrase common in the UK

Yes, it's common. I would however say that the phrase "I think I'll pass" is more common (at least where I live) and versatile; for instance, you can use the latter when rejecting an offer or expressing that something does not please your taste. "Are you going to our next lesson?" "Actually, I think I'll skip it." (don't skip lessons kids) "Would you like a cup of tea?" "Actually, I think I'll pass."|Yeah i would say so if you're talking about not going to an event or something similar. some people also say 'I think I'll give it a miss'

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