"size"

[Odessa Dawn]

Mr Willetts’ decision to recommend to the Privy Council that they be allowed to call themselves universities follows an announcement in June that the minimum criteria for a university of 4,000 students should be reduced to 1,000.

“It is right to remove the barriers preventing high quality education providers like these calling themselves universities because of their size.

More: Ten new universities to be created in single biggest UK expansion for decades

I do understand from "the minimum criteria for a university of 4,000 students" that size means the total number of people in a group not the total amount of physical space, am I right?

[Grumpy]

Yes.
Incidentally, in the phrase "the minimum criteria for a university of 4,000 students should be reduced to 1,000", the word "criteria" is wrong, as it is the plural. The singular "criterion" should have been used.