that depends on the country you are applying to. In Italy for example there is rolling admission, while in UK as you mentioned you have specific deadlines, normally concentrated in the period September – December.
For new graduates, usual starting dates in Europe/US are September and January. Statistically, many interviews take place in September-November (January intake) and January-March (September intake). The best period to apply as a new graduate is the first month of the period when interviews take place, since the process just reopened and you will have less competition. Thus, that would be September for the January intake, and January for the September intake. Having said that, you should check for the specific deadlines of the programme you are interested in, as they may vary by country. The best period may also depend on on-campus recruiting, which for undergrads is usually in September-October and for MBA in January-February.
At the following link you can find some additional information on the best time to apply: