I decided to write a "manual" if someone (including myself) has experienced similar problem to get access to the UKVCAS website.
1. To set up an account or log in into it, you have to accept cookies and tick "Continue" box on the top of the website.
Otherwise "Set up account" or "Log in" buttons will remain inactive.
Please note that if you use the browser add-ons like "I don't care about cookies" to remove these cookie warnings, cookie information will not show up and you will be not able to go further.
Just disable/remove add-on in the browser and refresh the page.
2. As a Firefox user, after logging in, the website could not load properly and the screen looked like this:
I fixed this by changing Firefox's privacy options. Go to Options/Privacy & Security/History and tick "Always use private browsing mode".
I hope it will be helpful for some of you.
Cheers,
otuel