I came across this blog. The blog says that if you have a valid/non-expire work permit of EU or Schengen member which I assume UK is part of EU, you can travel for up to 90 days to Greece. I hold a Tier-2 work permit visa in the UK. I know blogs cannot be trusted and I should check with the embassy directly which I will call them on Monday. I just want to check if anybody has done it before? Or it's simply not true.
Your UK work permit is not valid to enter the Schengen area, also for short time.
The exception for non-UE nationals living in UK is to hold a UK residence permit indicating "family member of an EU citizen".
No, you cannot enter the Schengen area only with a UK residence permit if you citizenship does not allow you to visit without a visa.
A possibly source for the confusion is that a residence permit from a Schengen country (including most EU countries but not the UK) does allow the holder to visit other Schengen countries without visa.
Another source for the confusion is that your UK permit does allow you to transit to a non-Schengen destination at a Schengen airport, even if you would otherwise need an airport transit visa (this would only apply to citizens of a much smaller set of countries than the general visa requirement to enter the Schengen area).
Finally, as Guido already explained, a residence card for EU citizens' family members exempts you of any visa requirement if you are traveling to another EU country with the relevant member of your family (but not if you are traveling on your own).