Hmmm... I'm fairly sure it always used to be no planning permission required... I believe there have been changes though.
But it's still a "portable" building, so to speak... there are rules about how far away it has to be from the main dwelling I think, but other than that, it sounds like a brilliant (& fairly easily executed) idea
I reckon you'll be needing to throw a log cabin-warming party too
If I tried to build a log cabin in my garden, I'd have no garden left and it'd be flush to the house