First things first. Is the floor still moving? If it is, then the problems will be magnified if you just lay a new floor on top of it. I assume your floor is concrete, as your note does not say.
To answer your question directly, I would suggest a screed if you are accurate with a trowel or both if your are not. Use a 1: 5 / 1:6 cement : sharpe sand mix and get a 100mm wide level around the room. This will be easer to manage than trying to level the whole floor at the same time. Do this job on day 1. Adding fibres will add strength. Not really needed if you are laying it on a concrete base. Good idea though if it is going over insulation.
On day 2, infill the floor with the same mix, using the day 1 levelled perimeter as a guide for your straight edge. Start at the furthest area from where you will be barrowing in the screed from and level of a barrow load at a time. Tamp with your straight edge and trwol it with a wooden trowel. Try to get it as compact and level as your can. If there are a few hollows afterwards, now is the time to use your latex / self levelling screed. (one the screed is dry)
Cheers for the response. The floor I'm laying onto is concrete. It has some cracks in it but they appear to be quite old so I can only assume that they have stopped moving. If not I'm sure it will let me know LOL.
The 1:5/1:6 cement : sharp sand mx, If I'm correct I need to add water (or something wet). If so how much?
I think I'll put the fibres in anyway. From what I've read they don't appear to have any detremental affect on the mix other than to strengthen which will bode well as the mix gets thinner towards the edges.
DIY how to tutorial projects and guides - Did you know we have a DIY Projects section? Well, if no, then we certainly do! Within this area of our site have literally hundreds of how-to guides and tutorials that cover a huge range of home improvement tasks. Each page also comes with pictures and a video to make completing those jobs even easier!