Dave, I think it's more likely you have a duff connection somewhere or possibly a short circuit on the stabiliser supply. The indicator flasher needs the resistance of the bulbs to heat up its bimetallic strip, that's why they flash faster when a bulb is blown: it doubles the resistance. If it doesn't flash it's either worn out or there's not enough current going through it.
Dave as ethel said about the flasher unit and also here is something to check as i had this problem.
Make sure you have the correct wattage bulbs in the indicators.
I replaced my front 2 indicator bulbs with low wattage 5W ones. Although good in theory the new bulbs did not generate enough current going through the flasher unit to make it do its flashy flash thing. So I, like you, i had indicators that were just permantly on.