I agree with eggontoast about you not needing another amp, yours will do fine! I just spent yesterday playing with a headphone amp that was £900 and I couldn't tell a huge difference between that and my little portable £50 Fiio!!! And you have an Arcam.... honestly you are fine, it's the headphones that will make the biggest difference here.
As for your main question (will you notice the difference between Grado SR80i's and an £800 pair?): Well that is a huge question, it is all relative and personal. I can tell you that I noticed a lot going from £160 Sennheiser's to £600 Denon's but I have just come from a post where a guy did not. If you are unsure then you simply have to try them out for yourself somehow. If you can't and are afraid you will make a mistake you could try buying from somewhere that will allow you to return them if you are not happy, some good hifi shops will allow this.
I have to say that I strongly disagree with dalethorn's comment about the those Grado's being the best. I haven't tried either of those so I can't say anything specific to counter it but I bet he hasn't tried all the compettion so neither can he. Everyone hears and want's different things from audio so don't listen to sweeping statements like that. I have read enough about headphones to know that such a view is not shared by the masses. If you look at head-fi's user opinions on headphones the top scoring 'over-ear' headphone models in your price range are:
1. Audeze LCD-2 (£800)
3. Sennheiser HD-800 (£1000)
8. Denon AH-D7000 (£600)
18. Beyerdynamic Tesla T1 (£800)
The expensive Grados are way down the list. Now I am not saying that they are bad, I'm just saying that there is a good chance that you will not agree that the Grado's are the best compared to the competition.