Don’t worry – there are plenty of ways to find experience! For example, you could try contacting the London hospitals you’ve mentioned asking for a placement. However, hospital work experience is quite difficult to find so you could also try contacting GPs and care homes too. As long as you can transfer your skills to medicine, it’s how you reflect on your experience that counts.
You can see each UK medical school’s work experience requirements on this page here: https://www.themedicportal.com/application-guide/work-experience/medical-school-requirements-medicine-work-experience/
And you can find all sorts of tips on how to find other kinds of work experience here: https://www.themedicportal.com/application-guide/work-experience/
Hope this helps! 🙂