There is no copyright registration system in the UK, so no way to search. As copyright protects specific artistic images (or writing, recorded performance, music, etc) if you know the image your best bet it to try and identify the artist and either find a date of creation online or contact them/their estate. Copyright persists for 70 years after the death of the author or artist, which should help you determine if it's still active for a lot of things without much research.
Tina.