Launched by Prime Minister Theresa May in November last year, the scheme is a key part of the Government's CyberFirst programme. It is being run by a consortium of the SANS Institute, BT, Cyber Security Challenge UK and FutureLearn.
One of its aims is to inspire more women to take an interest in the cyber security industry, although this has not been exactly a runaway success, with female students accounting for just over a quarter of the initial sign-ups.
London is leading the way with over 2,000 students registered and taking part in the assessment stage, while there have been 600 sign-ups in Birmingham, more than 500 in Manchester and more than 300 in Nottingham.
The students will shortly be put forward to take part in the second stage, CyberStart Game, which will provide hundreds of hours of challenges and teaching to help train the country's potential young cyber security experts.
Minister for Digital Matt Hancock said: "I'm delighted to see so many young people are interested in cyber security and have tested their talents in this ground breaking scheme. Cyber security offers fascinating and varied career opportunities, and I encourage inquisitive students across the country to challenge themselves to see if they've got what it takes."
The deadline for those interested in taking part in the first pilot scheme is January 21.
SANS Institute head of research and development James Lyne said: "20,000 sign ups within six weeks of launch is an unbelievable result. We're very pleased with the results so far, but are keen to see even more students sign up to take part before the closing date."