Their management cited lead singer Hannah Reid's "vocal fatigue" as the reason behind the cancellations, reported Independent.
The band also comprises Dan Rothman and Dominic 'Dot' Major.
"Due to a lengthy touring schedule over the last year and a half, Hannah has suffered with vocal fatigue which has forced us to cancel, at last minute, a number of recent shows. In order to maintain Hannah's voice and all of our well being, we have made the decision to withdraw from some of our upcoming festival performances," statement said.
Earlier this year, the band pulled out of T in the Park, again because Reid had lost her voice.
London Grammar's If You Wait is one of the ten best-selling albums of 2014 so far.