From the way OP speaks about this it seems like he's not able to leave the school? If you're at a university, I'd suggest going to a public Wifi spot when you have some free time. Seeing that you're from the UK, it might be a boarding school, which might make it harder to leave (no clue tho, never been to one). In this case, you might try the following:
1) Tor - https://www.torproject.org/
Download the portable version found here. This will allow you to surf websites in as close to complete anonymity as you can get. You are connecting only to another computer running the entry relay, which will be a random person who is also running Tor. This way, the school can't block access to the Tor network unless they use a whitelist. Be aware that this approach is very slow.
2) Internet via Bluetooth Phone Connection
If you are able to connect to the internet using your mobile phone, you connect your phone to your computer via Bluetooth and surf the internet as if it was on your phone. This method means that you will never be communicating with the school's internet, but rather with your own cellphone connection.
BEWARE THAT THIS CAN BE EXTREMELY EXPENSIVE! Unless you have a very good mobile-internet deal, I would not suggest that you do this. Not only will the connection most likely be very slow, but you could end up with a very large bill from your phone company.
3) VPNs And Other Proxies
Getting a VPN like was suggested earlier in the thread is a good idea. I don't have any personal experience with VPNs as you usually have to pay for them and I'd rather use free stuff. The free VPNs are probably excellent for surfing random sites, but I would never trust that my facebook account password or anthing similar is safe when connecting through a free service unless it was very well known. Tor is an exception to this, since it is open source and checked by a large community continuously.
Free proxies are also very useful for random surfing, but be very careful about entering passwords when using them. Most are fast enough to view YouTube videos. For a decent list of fairly good proxies go to http://www.xroxy.com. There are others, but this is a good place to start.
IF YOU CANNOT CONNECT TO http://xroxy.com, Google the phrase "Xroxy proxy list" and instead of clicking on the main link, click underneath where it says "Cached". This will make Google display a copy of the proxy list the way it was when it was indexed.
To configure your browser to use a certain proxy: (Assuming Mozilla Firefox)
Go to Firefox --> Settings --> Settings by clicking on the orange button in the top left of your window.
Next go to the Advanced section and click on the Network tab.
Under Connection click on the Settings button.
In the window that pops up, select the Manual Settings radio button.
Fill in the IP address in the field that says HTTP and the port in the Port field.
Then check the box saying Use this proxy for all protocols.
Click OK and exit the settings menu.
4) Google Proxy
THIS DOES NOT WORK FOR FACEBOOK OR OTHER "LOGIN REQUIRED" SITES!
If you just want to read sites like FML, Cracked, Etc. Then this might be enough. Simply google the site that you want and instead of clicking on the main link, click underneath where it says "Cached". On most popular sites, this will give you a fairly up-to-date page.
I hope this helps.


