How can we say 

 

Cannot watch tv in peace (maybe because of noise outside)

 

OR

 

Cannot read in peace (maybe because of children playing in the room)

 

So 'in peace' means unable to do something because of lack of privacy and being disturbed by something.  

Not sure about 'in peace'. We usually say, 'I cannot concentrate/have no concentration because of the noise', (or whatever is bothering you).

ไม่มีสมาธิเพราะเสียงดังมาก

Yeah but there must be something for 'to be left alone to do something.' Cannot study in my room in peace for example. 

Why not translate undisturbed? Seems to me a good word: ไม่ถูกรบกวน

Yes, that's very helpful thanks.