Sky don't make subtitles available on their On Demand programmes. They could (there's not an issue with file sizes, though they sometimes try to suggest that). But they don't, simply because they don't HAVE to.
It's really frustrating for me and many other people. 1 in 7 people in the UK have hearing impairments. Having subtitles on TV has been a life-changing thing for me - I scarcely ever watched TV before it became widespread a few years ago. Having them there means I can enjoy programmes with the rest of my family. If they're not there, I'm completely excluded. There's legislation that forces terrestrial programming to have a certain level of subtitling, but it doesn't cover a lot of other programming. I don't want another generation of hearing-impaired children to grow up excluded from TV, as I was.
I got sent this petition about it, and encourage you to sign it if you agree.
petition to put subtitles on Sky On Demand