One option to consider is a Now TV (owned by Sky, but has 'Movies', 'Sport' and 'Entertainment' options), which has players for ITV, BBC, 4oD and Demand 5 (+ YouTube, TWIT.TV {This Week in Tech} and a load more to download from the App Store).
NB It is a Roku player but manufactured only for Now TV (so it does not offer any other film services like Netflix), but is significantly subsidised down to 9.99.
I just saw someone on Ebay selling the Now TV box with 3 months Movies subscription (you can choose to cancel that, else you'd be on a rolling monthly contract) for about 18 quid (they are 25 quid in the shops).
I got a couple in the summer when they were 12.50 with 4 months of the 'Entertainment' service (so there are box sets of Sopranos, 24, etc, etc, and catch up from Sky 1, Sky Atlantic, Sky living, Sky Arts, and many live shows available too, but not all).
The box comes with a power supply (uses tiny amount of power - about 5W - so no on/off switch, HDMI cable and remote control).
At under 20 quid, I think it's probably a good starting point, so long as you have wireless router with a moderate speed (I think they expect it to have at least 2.5 Mbps download speed, and the majority of the country gets 5 to 75 Mbps now).
HTH. Sorry, don't have an iPad and have not used Amazon Prime/films service.