A compass and a signal mirror often end up in the same grab bag or coat pocket, but they solve opposite problems. A compass tells you where you are heading, letting you navigate cross-country, find a bearing off a map, or simply keep walking in a straight line when cloud or dark takes away the horizon. A signal mirror does the reverse: instead of helping you move with purpose, it helps other people find you, flashing a beam of reflected sunlight that can be seen for miles by search aircraft, hillwalkers or passing traffic.
For UK preparedness the two are complementary rather than competing, and neither is a substitute for the other. A compass is genuinely useful on most walks and in most emergencies where you need to move toward help. A signal mirror is a much more situational tool, only earning its keep once you are lost, stranded or need to be seen from a distance, such as after a car breakdown on an exposed road or while waiting for mountain rescue. Both are cheap, light and worth carrying together: a baseplate compass costs from around ten pounds, and a small signal mirror only a few pounds more, so cost is rarely the deciding factor.