Let= (1) to rent your house, flat etc. in return for money: ‘During the holiday season we let the cottage to tourists.’ (2) to release from or as if from confinement: ‘This sealed door won’t let the water come into the basement.’
Give permission or allow sb to do sth (WITHOUT to): ‘Why wouldn’t Alice let you help her?’ ‘Do you think your parents will allow you to go to England?’