This is actually a bit of a scare story run initially by the Telegraph which has a political agenda: it's anti Europe generally and anti the current Greek government.
If you check the British government page which they quote it actually says exactly the same as it says for every other country: essentially that people should not rely on just one source of money while abroad and should ensure they have enough ready cash for any emergency. This is clearly good advice but isn't being given specifically about Greece.
Without getting into the politics there is a chance that Greece will exit the Euro at some stage. If so it is likely that all parties will try and engineer a soft landing. When Cyprus had a credit crash a couple of years ago the cash machines were down for a couple of days but then things got back to normal.
I'm not trying to say there's no reason to keep an eye on the situation. (We're off to Andros at the end of next week and will probably keep a little more cash in hand than normal.) On the other hand I don't think there's any reason to really worry.
Alan