For the uninitiated, 1600 euros is about 1981 dollars.
That case takes up a full 1/6 of your budget, and isn't really the best case for air-cooling. 
These are some of the most highly rated cases on newegg. The 800D does have some nice cable management though. 
Wherever you're buying it from is 40$ more expensive than Newegg's, despite conversation rates.
The power supply is only bronze certified for efficiency (not sure if relevant in Europe), this 
Seasonic is gold certified and only 20$ more expensive.
For video editing, an 1156 i7 would be best. 
Here's a faster, unlocked i7 for 66 more euros. It's not an awesome price, but you'll want hyperthreading for video editing. Alternatively 
here's a slightly faster, locked i7 for 30 more Euros.
The only set of corsair memory I can recommend is 
this as it's 1.5 volts and 1600 speed. However, it is 165 dollars for 4 GB, while a comparable set of G.Skill 
Ripjaws is only ~92 dollars for 4GB.
I do think you can fit a blu-ray 
burner into your budget.
Here's a quick motherboard comparison between some of the better P55 mobos. This is just quick look at how that board stacks up, and is not inclusive at all.
A revised build:
Antec 900 100                          Much more reasonable
Seasonic 650 modular/750 watt model for 160/180           More efficient 
2x4GB 
Ripjaws 200 (before coupon code for 20 off) Cheaper, just as good
i7 875k 330                               Faster, unlocked, hyperthreading
Hyper 212+ cooler/
H50 50/80       Comparable performance
5850 320                                  (overpriced, but I'm unable to find reference for cheaper)
Blu-ray burner 130                      one time expense, carryable to next build
Ga-P55a 
UD3 or 
UD4 130/175        Cheaper, better ratings, UD3 for non-crossfire, Ud4 for
Samsung f3 70                            better ratings, cheaper
1490 USD/1202 euros. (assuming the hyper 212+ud3, H50+ud4 add 75USD/60 euros)
The things you want:
Cardreader: AFT PR0-55U Ultra Hi-speed USB 2.0 Writer    40,36
VGA Cooler: Thermalright HR-03     36,94 
VGA Cooler fan: Enermax T.B. Silence 9cm    4,99 
Add about an another 100 euros. I didn't include the fans as the Antec comes with them, and I didn't include the controller because it's not necessary to manually adjust fans, the 900 uses molex anyway.
Your possible increases in expenditure include: 800D case+lots of fans,  custom watercooling, X58 platform.