Monetarists point to the 1970s where there appeared to be a breakdown in the Phillips curve.
The UK experienced stagflation which is a period of rising unemployment and inflation
Keynesian would respond to this by arguing that the Phillips curve had merely shifted to the right because of a rise in structural unemployment and structural inflation. For example in the 1970s there was an increase in cost push inflation due to rising oil prices and powerful trades unions
Recent evidence in the UK shows us that both inflation and unemployment have fallen since 1992. This suggests that there is not a trade off but that it is possible to reduce both if there is suitable supply side policies