I'm not sure the people who posted above read the initial post completely.
He said he wanted to play/stream dota 2 at 720p this does not require spending anywhere near £400.
Dota 2 is very easy to run on high settings.
At 720p it is even easier. From
this benchmark you see that at a 1680x1050, even higher than 720p a 650 gets 62+ fps at highest settings.
So if 720p dota 2 is your maximum requirments your best bet would be to get a second hand card like the nvidia gtx 460(better than 7770) which sells on the bay for around £45. If you wanted new a AMD r7 250(10% worse than a AMD 7750) will cost around £60. The 460 will be significantly better so I would recommend trying to pick one of those up. It also overclocks like a beast 20%+, I know because my brother owns one. This GPU will be overkill for what you want to do but is still very cheap.
Now if you want to instead play new games at high quality at 1080p 60fps then I would recommend a AMD R9 270 for £125.
It has the best value out of all the cards especially as it will overclock to 270x performance with no effort.
So your integrated graphics would be up to the task.
Unfortunately, your cpu will not be upto 720p streaming. An 8 core AMD cpu should be more than up to the job. It will also do very with a very good GPU in all games.
I would recommend you get an AMD 8320(£97.25 if you go on google shopping) with a cheap £40 micro atx motherboard like the ASRock 960GM/U3S3.
I do not recommend overclocking as it requires a more expensive motherboard + cooler but it is an option to spend £20 more on a motherboard now and then buy a cooler later when you need more performance.
For around £185 you would be easily over your goal.
Parts:
AMD 8320 CPU ~£100
460 1GB Second hand ~£45
ASRock 960GM/U3S3 ~£40
(Unfortuantly none of these prices are from overclockers as they either are not competitive or do not stock the item)
As for an SSD it will not improve game-play or streaming but will improve your pc for general use with reduced application loading times.
I would recommend a 120GB Crucial M500 (£55).
Be aware that the 240GB version is available for £30 more from the rainforest so offers much better value, but you really only need the extra space if you want to store a lot of games on it.
Feel free to pm me if you want some extra help