I have found myself with a surplus of cheese, and I'm wondering whether it is possible to freeze cheeses like Edam and blue vein, and whether this affects the texture or the taste when it's thawed?

I don't know about blue cheese, but cheeses like Edam, Colby, etc tend to become crumbly on thawing. I don't think the taste is appreciably changed.

I have only ever frozen Camembert and Brie - absolutely impossible to tell they are frozen. But that isn't much help with regards a Blue and an Edam sorry. What is the best before for the Edam - as I find normally the hard cheeses have a good 12 months on them?

I have frozen edam many times and for long periods...I have mass grated it in the food processor and bagged, then use as needed. Never had any issues.

Many thanks everyone for this helpful advice! I had already opened the Edam and used some before the gift pack of cheese arrived, so grating it before freezing it is an excellent idea, and that's what I'll do.

Grate idea ;-) with grating cheese prior to freezing - lots of uses. I always have small stubs in a bag in the freezer - I pop them in to cheese sauce recipes, pasta dishes ect - works well.
Vanessa