According to [1] in 2012 for the UK renewables provided 11.3% of electricity demand and 3.94% of total energy demand. It's an important distinction, because petrol natural gas and jet fuel aren't renewable.
MacKay is the author of a book - "Sustainable Energy without the hot air" - which lays out all his calculations and the rationales behind the inputs. And it's available online [2]. So if you want to audit his calculations, have at it!
I've looked at the book, there's when I checked his figures and they seemed to disagree with reality.
So, electricity is about 1/3 of total energy. The 15% figure is the latest one for the last quarter of 2013[1] (PDF, see page 13). That means that (according to Prof Mackay) 5% of the UK is covered in renewable electricity generation.
MacKay is the author of a book - "Sustainable Energy without the hot air" - which lays out all his calculations and the rationales behind the inputs. And it's available online [2]. So if you want to audit his calculations, have at it!
[1] https://en.wikipedia.org/w/index.php?title=Renewable_energy_... [2] http://www.withouthotair.com/