welcome to GoY.

we had a similar problem when we moved here and we hired a mini digger to do the soil removal.
We built a retaining wall and use 2x2 plants of wood to make sure we got the levels. We then in-filled with bought in top soil.

The wall is 1.5m high and runs 15m by 3m. Turf etc was then laid once the soil had settled for 4-6 months over the winter.

How deep will the deepest bit be?

Alternatively you could terrace it so you have different levels

Another thought - Why not remove all the turf first (professionals somehow manage to roll it up...), keep it damp. ie alive, and then you can put it back after the level change and save lots of lovely lolly ? (Unless you are professional enough to leave it to settle like Seaburn...)

I think the lowest part is just under 2meters.
Great pointers though so thank you.
My only worry is the Norwegian spruce tree which I am keeping and do not want to damage. My fear is when taking up the lawn it’s going to be a web of tree roots from it and also some others that I am in the process of stump removal.
Although it would save money I think the lawn is too far gone with moss and weeds 🙈

I will keep you updated with my progress as there will be more guidance required ☺️