I just signed up to BT sport in HD on Sky. Thinking I might get BTTV
starter box - if I do how do I change my Sport to BTTV and cancel Sky?
You need to call up and do it, you can normally do it all as part of placing the order by phone.
Given that AMC have multi screening of the programs if providing subtitles by option is not currently feasible then I don't see why one of the overnight early hours repeats could not be a hard subtitled version that those who wish or need subtitles can record.
I suspect because it's expensive. As you probably know, the size of a channel's turnover is part of the criteria Ofcom uses.
As for providing them on in-house productions, that doesn't seem unreasonable because the AMC.com (US) website saud
"Does amc.com offer closed-captioned episodes and live content?
You can always count on AMC originals being closed-captioned whatever device you use. AMC is committed to providing closed captioning for our hearing-impaired viewers."
So English language subtitles do exist. Maybe there's a technical difference which stops the US ones being used?