Are there any free hairdressing short courses in or near london?
Nothing is “free”. You will be able to find short courses at community colleges or schools. Sometimes a salon will put on one-day “seminars” about a certain topic. If you want to know more, you may want to get employment at a salon, and get their training that they offer to the staff. It all depends on what it is you want to learn, what you are going to do with it, how in-depth you want to go.
