I did this last year. After applying for the non means tested i decided to change to means tested. I was told i needed to fill out another form including proof of family income. Ring up ur LEA and they should tell u what you need. Most of the time you can download the forms from the website. After changing I managed to received everything in time after enrolling. As your changing the amount you want it should not take too long, as long as you include the relevent docs.