Interesting, from an equality law perspective.
Under EA 2010 positive action is legal
https://www.legislation.gov.uk/ukpga/2010/15/section/159
I saw recently for example that the Law Society provide eight-week (!) paid internships under the 10000 Black Interns scheme.
This I understand is legal on the basis that it's "only an internship", and the actual "employment" is open to all, so this falls within legitimate activity, and
s 159
(1) [The Law Society] reasonably thinks that—
(a)persons who share a protected characteristic suffer a disadvantage connected to the characteristic, or
(b)participation in an activity by persons who share a protected characteristic is disproportionately low.
So the "10000 Black Interns" program is legal for law, because s 159(1)(b) is met.
However, the "no graduates" rule is indirectly discriminatory on the grounds of age. It has the effect of saying "we don't want people aged over 21/22 on our VS", as the number of undergraduates over 22 would be vanishingly small, so it would be indirect age discrimination, if
"it puts [people who] share the characteristic at a particular disadvantage when compared with [people who do not"
As this is indirect rather than direct discrimination, the test is "proportionate means of achieving a legitimate aim."
So I think there would be two tests:
1) does the exclusion from the VS put mature candidates at a particular disadvantage - they could argue TC route is still open, and therefore "not a particular disadvantage", and perhaps point to relative prospects of success via two routes
2) is it a proportionate means of achieving a legitimate aim.
I suppose they might argue that it's somehow proportionate in that graduates need to be tested more thoroughly, but it seems unlikely to me.