Is this a problem for e.g. account.bbc.com though? I can't see how that can impact bbc.com/bbc.co.uk if the header is set on the subdomain only.
I remember it used to be that e.g. news was accessed via news.bbc.co.uk but this seems to have been changed more recently to be accessible at /news. As you note, this makes HSTS a no-go because of all the other products on the same domain need to support HTTPS. This makes me wonder why this change was made in the first place. It would also seemingly mean that (without e.g. https://w3c.github.io/webappsec-suborigins/) an XSS in one product means an XSS everywhere.
I'm sympathetic re. the SSL configurations you need to deal with and it's reassuring that this is being worked on.
A few years ago a decision was made that the BBC site should be all under www.bbc.co.uk, I believe this was mostly for marketing purposes, but also to simplify our internal routing for the site. news.bbc.co.uk was previously separate as News had it's own infrastructure separate from other parts of the BBC, but that's been rationalised now (leaking subdomains for technical reasons was something we frown upon).
I realise this is being worked on and somewhat tangenital to this post, but the BBC's rollout of HTTPS has been shockingly poor and incredibly slow comapred to other news organisations. What's the point of serving account.bbc.co.uk securely if all links to sign in can be MitM'd? The parts that can be accessed with HTTPS don't seem to use HSTS either.