whats your status right now? it is all dependant on your status.
1- if married to uk citizen you can study and engage in any work you want and you dont need any visa .
2-if not married to a uk citizen :

i believe new regulation doesnt allow visitors to switch to student visa.
also, usually you cant get a student visa for a part time course(it has to be more than 15 hours a week to be qualified for a student visa)
processing time vary from 3 to 14 weeks, if needed you can apply at any PEO for £500 for same day service.
if you be more specific i will very glad to help you