you can not just go and build a cottage anywhere you like you need planning permision,i think the heath comes under camden council. why not try to contact there planning department first before getting the builders in
Cottaging can apply to heterosexual activity too, but mostly it is used in the gay community.
Anyone caught in a sexual act in a public place can be charged with indecent exposure. The best way to enjoy this if - from your question - you are considering it, is not to get caught.