Not at the moment, but nowtv have officially confirmed this feature is coming to nowtv this year.
There is a short paragraph in this Sky press release about downloads here.
If you like to get your TV fix on the go, NOW TV also announced it would be rolling out downloads to the NOW TV app across mobile devices for its kids, entertainment and cinema passes, starting with the Kids Pass this spring.
The Sky press release link on my post above didn't work for some unknown reason.
Try this link below if you fancy a read.
This seems to have confirmed that we will be getting the download function before Christmas. However no confirmed date for when we will be getting it, better than not at all though!
Sounds like a HDMI HDCP conflict between your TV and NowTV playback device.
Have a read of this help guide linked below which may point you in the right direction on how to fix it.