I've heard conflicting reports of this. Some say ancient Britons were only introduced to the bow after invasions by Germanic tribes, but others say they were aware of the weapon before this. Is there a definitive answer?
There have been at least 6 prehistoric bows found in the British Isles - 3 in England (Meare Heath, Ashcott Heath, Eddington Burtle), 1 Scotland (Rotten Bottom), 2 in Ireland (Barrysbrook, Drumwhinny Bog). For a summary and references to publication covering these finds, see http://www.ucl.ac.uk/prehistoric/past/past46.html#Bowstave
There have also been many finds of arrowheads, Neolithic, Bronze Age, and Iron Age. While at the time of the Roman invasion, the sling was a much more important military weapon, archery was in use (judging by finds of arrowheads - they are present, even if greatly outnumbered by slingstones, in hill forts).
In any case, the Romans used the bow, and would have introduced it to Britain before the Germanic invasions, even if it hadn't been known in pre-Roman Britain.