Yes
If you know what you want to do, start looking now. If you want to get into finance there are lots of pre-Christmas deadlines. The same with advertising. If you are interested in the public sector, there are November deadlines for Fast Stream Civil Service and NHS Management, amongst others. Check CDEC’s Jobs for Finalists and our list of other jobs sites. Some sites list jobs by deadline (Milkround, Inside Careers)
No
Don’t panic! You may be able to register for email updates or subscribe to RSS feeds for the latest jobs in your chosen sector/s (Targetjobs), so you won’t miss out. Don’t take a scattergun approach and start applying for everything. It’s better to spend some time working out what you want to do, and researching employers, then make a few quality applications
See Also:
CDEC’s list of early graduate deadlines (.doc)
IPA Graduate Factfile - graduate schemes in Advertising
Efinancialcareers on why you should apply early - for investment banking