You do not need any specific qualifications to become a market trader, although basic Maths skills and English are useful. Your personality and ability as a sales person is more important than any other qualifications. Also you must be over the age of 16 to trade on a market stall.
Sometimes it's difficult to get a regular stall on our markets. so you could start working part time on a market stall, by gaining experience at an established UK market, you could then attend a market as a casual trader, eg. arriving at the market early which could then lead to becoming a regular market trader.
The qualities and the skills set a market trader should have when running a market stall are:
What further training and development can I do?
Most of your training to become a market trader would be informal and involve learning on the job from experienced market traders, sharing their knowledge and observing their sales techniques.
There are some short courses you could do, which are mainly provided by the local authorities. You may find it useful to do a course in a subject such as running a small business or book-keeping and accounts.