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The Trust says women would be more affected than men, while those from poor backgrounds would be hit hardest.
It says the freeze would compromise government pledges on social mobility.
In July, Chancellor George Osborne announced a consultation on freezing the threshold for five years, rather than linking it with average earnings.
This would affect those who took loans from 2012, when annual tuition fees were raised to a maximum of £9,000 in England.
Read the full report here