It is doable - the layout is pretty much the same as my uni room apart from the monitors are together. To do both systems on the same setup, the best way if you can afford it is to get an amp and hifi speakers. It's a higher initial outlay, but the speakers should last you a decade, and it gives the best flexibility.
What you need:
AV Receiver - second hand is probably your best bet. You can get a decent Onkyo for £150 with HDMI switching. I got the SR605. Just look for anything that has enough HDMI ports for your use
5 speakers. Ideally you want a matching set of centre, left, right front speakers, and probably a smaller matching set of rear speakers.
Subwoofer.
You're looking at £250 for the 5 main speakers, 100 for the sub and 150 for the amp - so £500 overall.
HOWEVER
You're a student and presumably looking at how to do this cheaply can do the system for less. I found that actually the sub was overpowering in a uni room... 4 decent bookshelf speakers provide ample bass: all I did was turn the bass up on my amp and it has more bass than any of my friends' 2.1 systems.
Similarly you don't actually need 5.1. The left and right front speakers can work together in stereo to provide the sound from the centre speaker. You just need to make sure that they are the same distance from the monitor. I'd advise adding a centre and a sub later on, when you move to a bigger room: but you REALLY don't need it yet.
So the system can be done for £350. £50x4 speakers, and £150 for a decent amp: possibly slightly less.
You don't state a budget, but it's a brilliant way to do a system if you have the £350.
In terms of placement, you would be best off moving both monitors towards the corner of the desk, and placing the front speakers each side of them, centred on the film TV. The rear speakers then go as close to the corners of the bed as possible - you want them in line with your ears if possible, but they'll work okay a bit further forward, angled behind you. A subwoofer, if you get it, can go anywhere in the room.