Problem Tenant

Possession - Section 8 and Section 21

Hi, We have a problem tenant who has caused complaints from others in the flat with his music and TV noise in the past. His neighbour moved out citing his noise as the main reason. We verbally warned him that if it happened again we would have to ask him to leave. Since a replacement tenant moved in things seemed to have settled down, but we have recently had very similar complaints from two tenants about him. They are now saying he's smoking week as well.
He has finished the six-month initial period of his AST, now on to a statutory periodic tenancy.
Is it possible for us to simply write to him and give him one month's notice to leave, or do we have to go down the path of Section 8 or 21 court proceedings? Our concern with the 8 & 21 route is the time it looks like it would take, and what the other tenants will do in the mean time.