The Transport Authority have finally abandoned their fruitless attempt to banish buskers from the Underground, and in a wonderful volte face, they have provided special pitches, and interview buskers to apply for them.
As advised, there is competition, because they can be quite lucrative, but if yoou are determined, and good enough - give it a go.
in the mean time, do try Covent Garden as a 'rehearsal' and see if you like it - or ask the local Tourist Information Office if they know any other spots where you can busk without a licence.