Having exactly the same issue. Downloads the new app, when I open it, it opens up the old app and when I click 'Let's Go' to download new content it takes me back to the page saying "download the new sky app today". Must have done this 6 or 7 times and the same thing happens. My guess is that the new app allows you to downlaod the content straight from the app rather than being directed to the website. However the new download doesn't seem to work so there is now no way of downloading new content.
Strangely the Sky Sports App seems to work.
Any advice on this would be appreciated.