My year 11 daughter applied for a place before Christmas or early January on one of these summer courses after she saw a poster up in her school. She applied online.
They were called the 2015 Inspire EDT courses. Cost £105
She had to decide if you wanted a residential place or a day place. Offers went out some time in March and she got a place at Queen Mary, University of London. The course lasts for 3 days.
I am not sure if any places are still available on this. She has not looked into any other courses, that I am aware of.
Maybe Imperial are offering other courses that are not booked up yet.