I’m in the UK, too, so I’m pretty sick of AsianCrush being advertised to me but not available to me to see what’s on it full…
As you happen to be in the UK, that gives me someone to tell that the online SQIFF from 5–18 October (rentals from which are on Vimeo, so it might be possible to download them for offline viewing in the Vimeo mobile app – that worked for me with my rentals from Nippon Connection earlier in the year, anyway) and London Film Festival from 7–18 October (though it definitely won’t allow downloads, as it plays in the BFI Player app, which never does even normally) will have some rare East Asian film and video available UK-wide temporarily. Leeds International Film Festival from 4–19 November might do as well, if that has an online programme.
Avoid downloading from Dramacool if you can. That arrogates pirated content, so as well as not supporting the content being made and subtitled, it’s also likely to inject malware onto your computer (or carry adverts or link to sites which do) and the Japanese authorities at least are planning on cracking down on international piracy of their content. Any amount that a subscription or rental costs is far less than one can be fined for pirating something you could have got on a legal service.
As I wrote, Viki seems to not allow downloading even with a subscription, but I think the mobile apps for many of these do?
https://www.amazon.co.uk
https://www.apple.com/apple-tv-app (can also download on desktops)
https://www.crunchyroll.com/videos/drama (downloads only with a higher-tier subscription)
https://www.youtube.com (but check that the content is on an official channel)
https://www.eyelet.com
https://www.channel4.com/categories/world-drama
https://www.funimation.com/genre/live-action/
https://vimeo.com/watch (can allow downloads for free, but it depends on what the uploader has set for each video – depending on what the uploader has chosen, they might allow a video to be downloaded on desktop computers in a web browser, only on mobile devices in the app for them, or not at all, and for free, for rentals, or only for purchases – and try to check that the content is on an official channel to make sure you're watching it legally)
https://www.viddsee.com (I think this might possibly allow downloads for free in the mobile app, but I haven't tried it yet)
https://www.dekkoo.com/international
https://play.google.com/store/movies
https://mubi.com
https://www.shudder.com
MangoTV (search for it in app stores; it doesn’t have an English-language website)
https://www.iq.com
https://www.vidfish.com
https://rakuten.tv/uk
https://wetv.vip/en