I think that you need to wait and see if new buds appear , you could gently scrape a little of the bark to see if its green underneath but don't do anything drastic until spring as some plants will shoot lower down if the top has been killed by the frost--I'm doing that with most things

Pamq is absolutely right. Last winter we suffered minus 20C here and I despaired about our bay trees. One was totally brown and did never recover, but a second which looked completely 'blasted' simply started growing again from the base in the spring. To look at it now a year on, it's as if it never suffered at all.
The second one was next to a stone wall, while the one that died was more in the open.
So as I doubt you've had temperatures as low as that in Northern Ireland, I would be very hopeful your bay will come back in the spring.

if the top is dead try cutting it down and see if it re-grows..