I don't think there is an answer keeping with the iPhone.
A possible low-cost option is to get a NOW TV box, depending on what you want to watch.
That will let you stream Free-to-View Channels direct from the various catch-up apps.
For Sky Content, you could get the Sky Movies from NOW TV instead of having Sky Cinema at home (I have Sky TV at home, but I have the NOW TV for Movies instead of paying Sky directly - it is about 40% of the price for the exact same movie content and you can watch on the TV when away without hassles).
You could get the Entertainment pack from NOW TV as well, but as it is virtually impossible to not have that with a Sky Sub anyway, you would end up paying twice for that lot.
Another 'half-way' house option is buy a cheap android tablet or basic laptop for the purpose and install/run the Sky Go app on that? At least instead of a 4" or so screen to look at you could use a 10" or bigger screen?
Finally, you could have a look at Slingbox. This is a device that effectively remotely controls your Sky box at home and sends whatever it is doing to your TV where you are, so you see the same as you do on your MH TV and can watch everything you do at home, including stuff on your planner (and if abroad I am pretty sure it gets round the issue of not allowing UK broadcast programs getting blocked without having fancy VPN setups).
I looked at this years ago so things may have changed but the slingbox product is still being made and developed so maybe worth a look?