We have quite a big newly seeded lawn on two levels, joined with a slope that gets increasingly bigger as you go up the garden. The bit you can see on the right here which curves up from level to about 18″ higher up by the greenhouse.

I was going to just get a decent self propelled petrol mower but the slope’s making me think I might need a hover mower of some sort.

We’ve a top end budget of £400.

Any recommendations?

Mower for the flat bits and a strimmer for the slope?

That’s what I’m thinking so far

Regular mower can manage that, just the transition from slope to flat on the bank that won’t be uniform.
Depends how particular you are over the finish. Just start with a regular mower and see if you like the result. Strimmer will tidy the transitions if they bother you.

Obviously, if going with the former, it won’t be suitable for showing new bike pictures on here.

Ended up with a 4-stroke, unleaded beast of a thing. Viking from the specialist mower place down the road. Already crashed it through my dry Stone wall

Already crashed it through my dry Stone wall

Excellent work, I love a story with a happy ending 😆