At 83.7 km2, Þingvallavatn is the largest lake in Iceland. Its surface is 103m above sea level, its average depth 34.1m, but it reaches a depth of 114m, i.e. 11m below sea level. Fed largely by underwater springs the water is always extremely cold, the only river feeding it being the Öxará, and the river Sog being its outlet. There are two islands, Sandey and Nesjaey, both old craters. There are many summerhouses around the lake. 
The exact location of the summerhouse used in the filming, thought to be on the south-west side  has recently been identified following an appeal in the Icelandic media . The article may be viewed here, and an article describing the filming at the summerhouse can be found here.
Images © BBC Scotland.
1. Steindórsson, S. Hálfdanarson, Ö. Hálfdanardóttir, E. (2007) Þingvallavatn – Vegahandbókin 2007. p196.
2. Sæmundsen, E. (2013) pers. comm 29th April 2013
3. Morgunblaðið (2015). ‘Sumarhusið fundið’ (20th February 2015 p. 18) © mbl.isÁrvakur hf.