The destabilisation of neoclassical tearing modes (NTM) requires a finite size seed island which is often provided by sawtooth activity. It is shown that the beta value at the onset of NTMs can be significantly modified by altering the sawtooth period using ICRH in JET. Sawtooth stabilisation, leading to long sawtooth periods, enables NTMs to be triggered at low beta value, consistent with larger induced seed islands. By destabilising sawteeth, that is with a shorter sawtooth period, larger beta values are required to trigger NTMs. This is the first clear direct demonstration of the relation between sawteeth and NTMs and opens the possibility of increasing the beta threshold by sawtooth destabilisation. Adding a slow power ramp-down, after the mode onset, shows that NTMs are metastable as long as the discharge is in H-mode in JET, emphasising the role of seed island control to avoid NTMs.