Peter Davison: ‘I think Doctor Who is a good role model because he’s a hero who doesn’t beat people up’

• When Peter Davison was 15, his parents gave him a book of Cole Porter lyrics. “I’ve always played the guitar and we had a piano in the house, so I’d bang out chords Paul McCartney style,” he says. “But mainly I wanted to be a songwriter. Because I am quite a traditionalist, Cole Porter always appealed to me.”