unsure what type of agreement I have, and hence how to evict

Good morning, new to the forum, hope you can help me. I think I've been a bit lax and am about to pay for it

I lived in my house (3 bed semi) and let 2 individual rooms on a monthly basis, sharing communal spaces with the lodgers. No formal AST was in place as I felt it was not required given the circumstances

I then moved out and let the 3rd room, but did not change the legal agreement I had with the existing lodgers (now tenants, not sure if there's a difference). I'm now unclear what type of agreement I have with those 2

One of those lodgers is now causing problems with the other tenants and I want to evict, and clearly I want to follow the right process

- is the agreement now an AST by default as I no longer live there?
- is the agreement an excluded tenancy as that was the original basis of the agreement?

Going forward I'll arrange formal tenancy agreements. When I was a tenant myself, I received a section 21 notice (I think) alongside a new agreement, is this good practice? I suspect that simplifies the eviction process if necessary, without commitment to evict..?

Thanks for any advice