On demand/streaming, what am I missing?

[MrChips]

To help stop this turning into a massive rambling post..... I've got the following equipment:

Sony 46W905 TV - set up wirelessly, but I don't use any of the apps
Humax HDR1000S - Freesat box, connected via ethernet cable. This has Youtube, iPlayer, 4OD which all work well.
Apple TV, connected wirelessly
BT Infinity internet connection

And here's the problem, i'm keen to make the use of 2 things:
My Amazon Prime subscription,
BT Sport

But can't find a way of doing this in HD, or even decent quality! Trying to run the mirror function on the Apple TV from my Macbook is incredibly jerky and unreliable, and AmazonPrime also says that HD isn't available on this device? Is that something specific to a Macbook?
I've tried all settings with my router (BT HH5) but nothing seems to improve the jerkiness. Watching the actual content on Apple TV itself is fine, so it must be something to do with the speed between the macbook and router?

BT Sport - Any devices (apart from Sky) that have this available or easy to run this onto the TV? They have an App for the phone, but mirroring this via the AppleTV means the screen size is compromised.

So, what am I doing wrong? Any advice?

[rsv gone!]

Wifi isn't much cop for HD.

Get a long cat 5 cable from ebay and try plugging the tv straight into the router.

[Bullett]

I get HD over wifi from both Netflix and Amazon (what they call HD at least) it's very crisp and smooth. That is via a FireTV.

[MrOrange]

No worries mirroring to ATV in HD for both BT & Amazon - but I use my phone or iPad. Smart TV apps on my Sony now gives me Amazon/Netflix in HD.

Both scenarios even work over 5mb 3G connections (just moved house so no broadband atm)

[belleair302]

It is possibly the router is throwing off interference, or the surrounding cables.