I’m in the process of building up my first computer and am a bit stuck on graphics cards. I was thinking under £80, I won’t be doing any gaming, just HD video watching and a bit of editing.
I’m going to be using an AMD FX-6 Six Core 6300 Processor with an AMD 970 chipset if that makes any difference.

NVidia 1GB 460 would do that and be able to play many games too.

(I don’t know much about this, but…)

Are you sure that 6 cores are useful to you ?
If you’re not multitasking lots you might not see the benefit

Intel processors have enough internal graphics for watching HD video without a separate card (my 15 does anyway) – not sure about editing and what that requires though

If you decide you want a separate graphics card anyway, this guide is great for what’s the best buy at any given price point: Tom’s Hardware: Best Graphics Cards For The Money: March 2013

I would imagine you’ll be fine with onboard graphics if you’re not playing games but if you really want a card then 80 quid will buy quite a good one.

Be careful with your power supply as well if you’re using a graphics card. In built graphics should be plenty good enough for HD video – mine is!

If you think that your bit of video editing might get serious and you’d be using Adobe Premier Pro have a look at their website for a list of cards that support accelerated features.

The Nvidia 470 and 570 are on there but probably out of your budget even if you can still find somewhere that stocks them (the 6xx series has now been out for a while).

I’ve no idea if these features are worth having though!

http://www.adobe.com/uk/products/premiere/tech-specs.html

On board graphics will be fine (are these chips coming with a 7xxx built in GPU? Not very well versed on AMD chips at the moment). You do not need to spend much if anything on a separate GPU if you don’t game I don’t think. Even if you decided to go for one I’d go for a fan-less low/mid range one, my 460 is quite loud and annoying but I only use the PC for gaming. So something like a 7750 or 550 if you can find it still.