YouTube is based in California, it would be under US jurisdiction, not ours.
The terms of service for YouTube are tight. They include being above 13 years old, and "7.3 You understand and agree that you are solely responsible for your own Content and the consequences of posting or publishing it. YouTube does not endorse any Content or any opinion, recommendation, or advice expressed therein, and YouTube expressly disclaims any and all liability in connection with Content." and "7.9 You further understand and acknowledge that in using the Service, you may be exposed to Content that is factually inaccurate, offensive, indecent, or otherwise objectionable to you. You agree to waive, and hereby do waive, any legal or equitable rights or remedies you have or may have against YouTube with respect to any such Content."
I don't think anyone, UK or US, has ever managed to successfully take YouTube to court over content hosted on the site. I'll have a deeper look later, but essentially, they are a hosting platform.
YouTube Kids is slightly more regulated, but that wasn't being used in this case.