Hi There!
I think it's great that you are trying to get some work experiences in these fields that interest you.
My name's Josh and I'm an MA film student at Liverpool John Moores University, so I can offer some advice about the film/ media industry.
If it's something you want to go into/ gain experience, it's usually about who you know. Lucky for you, London is the most filmed in city in the whole of the UK, so there should be plenty of filming going on around the area.
The best place to start is usually LinkedIn. On here you should be able to find and connect with people who work for some filming companies. I'd suggest to look out for smaller ones, or perhaps post-production houses like Envy (as I know they do a lot of work with students) and send them a message to ask if you could shadow someone for a few days/ get some work experience.
Here is a list of all the production companies in London-
https://filmlondon.org.uk/resource/production-companies so it should be useful for you to start contacting some people.
Of course you could apply for internships and placements but they are very competitive, and honestly, this way is the best to get your foot in the door and start making connections as it's more personal, and more often than not, they will be more than happy for someone to go in and shadow them.
I hope this helps
Good Luck with the search for work experience.
All the best,
From Josh
Official LJMU Student Rep