Got a puncture yesterday, I noticed it as I go into the car so changed the wheel and put a winter tyre on, I knew the TPM would activate due to the winter wheel being smaller 205/55r16 as opposed to 225/50r17.

However it took quite a while before the alarm was triggered, I drove around 9 mile before being warned of low pressure in the right front tyre.

Is it normal for this warning to take so long?

For an indirect system, yes it is: http://www.my-gti.com/321/volkswagen-tyre-pressure-monitoring-system-tpms

 

If you want a quicker warning, you'll need a direct TPMS system with pressure sensors in each wheel