How can I stop a pyracantha from flowering?

You can't, unless you keep it pruned so far back it doesn't get a chance to flower. Perhaps you need to give it a good hard prune next spring, as much as anything to encourage thickening of foliage in the areas where you say its thin.

Could try feeding/mulching to encourage it to thicken up?

I'm afraid a pyracantha will flower and produce the red, yellow or orange berries which it is what people grow them for. Did you plant it originally? Maybe you should have considered an evergreen hedge plant that does not flower or flower significantly and is thick all year round like laurus.

We bought the plants from a well known nursery. They wre supposed to be all the same species. However, some are red and others yellow berries. About 2/3 of the hedge (30 metres long) is fine and, after about seven years, is thick enough. Some sections are pretty thin and, as I mentioned in the OP, look reasonable in April but thin out badly when the flowers appear (& then berries). We planted it as much for the berries as anything else but would like it to thicken up a bit first (as the flowering seems to be holding it back at present)
Thanks to Bamboo, Sid & Andrea for the replis!