Jackson and Foster, whose own bid for the company collapsed, said: "Babcock has chosen not to revise its offer to a level that in our opinion would recognise the value of the Peterhouse businesses and their prospects."
Babcock International has until this weekend to increase its offer under takeover rules.
So far, 47% of the shareholders of Peterhouse have accepted the offer. Babcock believes it does not need to improve the bid to win the approval of the extra 28% of shareholder it requires by the middle of this month.
With 75% shareholder approval, Babcock International can change key documents at the company, such as the constitution.