If I were you, I’d contact the BBC directly & just ask them - I definitely don’t recognize that as a famous piece or as the style of an older, famous artist. To me it looks quite recent. It’s possible that one of the BBC staff artists did it, or it could have been a graphic artist from whom they request commissions. I’ve had the impression that many news outlets commission their illustrations.
The other possibility would be to search via Amazon.com - they have links to some big poster companies.
Good luck finding it - it’s great to hear that you’ve been moved by art!
It doesn’t look like any artist that I recognise. I think it is a commissioned illustration or from a picture library. The BBC are usually good at replying but give them some time. It’s the weekend and they get an awful lot of mail. I can’t find a phone number for the BBC website.
It could be a stock image. Of the two agencies I usually start with, Getty Images turned up nothing, and Corbis was down for maintenance – you can check with them later yourself. And if you’re really interested, there’s a whole passel of stock agencies listed on creativepro.com that you can look through. (I know it says “stock photography,” but many of them will also carry illustrations.)