What sort of funding are you hoping for? Research Council studentship schemes have a closing date in Dec/Jan and all will be advertised from about October. Other adhoc studentships will be advertised as and when. Oxbridge has a system all of its own and seems to have a very early Jan deadline nor just for funding but for place.
Yes, you can apply 'early' but this doesnt mean you are any more likely to get funding - it isnt 'first in first served'. Take time to identify that the dept has the right academics/interests and what their funding is/how it works. Just firing off an application with 'I'd like to be considered for funding' in October wont be what matters. Have you emailed any likely academics with a brief 'this is who I am, this is what I's like to do, is this the sort of project/topic your dept would be interested in?' type email. If it is, then follow this up with a 'I will need funding, what is available and when should I apply?' email. Applications arriving out of the blue usually are not as successful as those that follow up contact already made. Have you written the best application possible? If you are still at Uni then its a good idea to show your 'statement' to a friendly academic for comments/advice - and their advice about the Uni/dept you have approached. And, of course, you must tell any referees what you are applying for, and ask them if they would like a copy of your 'statement'.
Much of the process of getting funding is gradual and is almost like a form of 'flirting' - academics like being approached by potential students (its an ego thing) and if they like what you are suggesting they will 'push' for you in any competitive funding. Even if you are applying for a specific advertised project studentship then an email 'This is my background, does this fit what you are looking for' email is also sensible. Short emails, or chatting to them at conferences etc, is always the way to start, and before you actually put in an application.