Yup, bad idea to put all your personal info on the public web. But whatever, it's a link to your site not posted here on the site.
Programmers generally don't have a video demo reel, but it is somewhat common to have a portfolio of projects on the web site. You have that, and they look reasonable.
For the CV, since you are in the UK there are regional differences. In the US I would recommend you eliminate the "skills" section, and use the space to describe what you did in your courses that are transferable to the job. You have a section incorrectly named "Experience". That is shorthand for "Work Experience" which means "somebody paid you a regular wage to do this work every day." Those are personal projects, which should be used as the section name. You have "Work Experience" later on the page which is used correctly.
Intern and junior positions are relatively rare. You need to be looking at the same time that a local company happens to have a need. The few companies who hire them don't hire them legally as intern roles because of the legal requirements, instead they hire them as a junior developer over the summer or for a short contract. Legally, "interns" need to not do work that replaces a regular job, and they need to be supervised about the same as if they were a student, and in exchange they can be unpaid or paid less than the minimum wage. Generally it should also be affiliated with a school.
Overall what you have looks reasonable for an entry-level programmer. The next barriers are simultaneous needs (you applying for the job at the same time a local company is looking for a worker), then being the best candidate among all those who are interviewed. Small studios are generally the best work environments but they rarely hire junior level or intern workers. Larger companies may hire a few entry level workers for a large project, but you're looking at perhaps one in twenty or one in fifty. The jobs are far easier to find if you have some connections within the industry who can put your name out to their teams and team leaders. They may be able to create the position if they were thinking about the role due to pressure but have not actually started hiring yet. That is the most effective way to get a job; I've read that working your social connections is about 9x more effective than basic applications directly through the company.