First, let me respond to the first comment. Could you explain why LSE would find it useful if a student traveled during his/her gap year? I'm not attacking you, I just never understood why people did that and think it would significantly add to their CVs.
Now to the poster, I would suggest you start sending out some applications. Be bold and confront a few companies. I understand that it might take a while before you land an internshiP somewhere. You could decide to travel A BIT and await some of the application responses, but don't fill your entire year with leisuring. If the internship doesn't work out, apply for volunteer work. Or organise something, schools love to see you do sOme extracurricular activities. Preferably something that is at least a bit relevant for your field of study. In 2010 I almost decided to go for a MSc at Edinburgh, but I hesitated too much and decided not to in the end. A department director advised me tO fill some more time with relevant work experience. So I took a gap year (sort of) and followed extra pure economics courses (I have a business ecOnomics background) and landed a part time internship somewhere. Result: with an average below that of the average LSE applicant, I got accepted to the MSc Environmental Economics, and I sincerely think my gap year cOntributed to that.
Hope this helps you out!