Thank you for correcting me, CF. Many years ago (in pre-USB days) I had an HP printer that accepted both serial and parallel connectors and I've obviously forgotten which one was the most common!
Anyway, I think that we're all agreed that it's not likely to be a Scart socket.
Like Rojash, I'd guess that the printer is likely to be quite old. At least 5 years ago, a friend of mine needed a new printer for her elderly (non-USB) PC. I couldn't get her a new one anywhere (either in store or online) and I ended up driving a 150-mile round trip to get the nearest available secondhand one.
Chris