It is to your advantage to apply early in some banks, as the HR team deal with applications as they get them and often more time is spent with those that are received early. Interviews are arranged and assessment centres set up and places allocated through the application period, so applying later can sometimes put you at a disadvantage.
Be aware that the majority of banks ask you to complete online tests. You have to pass these before they even look at your application. Its critical therefore to gain some practice before you take them. Obtain practice papers and advice HERE