raise Lawn about 15cm. A few questions

Hi, I'm new to this forum, I've had a good read through quite a few threads and think I've got a plan.
We moved here a couple of years ago and the previous owner had made a fantastic sectioned garden with ponds waterfalls and many cobbles lots of ivy bushes. It was very lovely but totally impractical for us with teenagers and a dog.
The plan is to put a lawn around the pond and remodel quite abit.now the questions one part of the lawn is about 35-40cm higher than the other from left to right and from the back of the house down to the fence. I'd like to level this out. Thinking bring the highest part down 10cm and raise the lowest up about 15cm. Not sure how to do this.
Thinking of turning the turf over and adding topsoil to try and get around level then turfing. Would this work? Its Bedfordshire and very clay ground, should I mix with sand & or stone?
I've got about 3x ton bags full of decent soil from where Ive already removed one of the raised beds and a higher pond
Heres a handy dark picture oll get some better ones! Need to get rid of all the gravel area and the circle for new grass
We moved here a couple of years ago and the previous owner had made a fantastic sectioned garden with ponds waterfalls and many cobbles lots of ivy bushes. It was very lovely but totally impractical for us with teenagers and a dog.
The plan is to put a lawn around the pond and remodel quite abit.now the questions one part of the lawn is about 35-40cm higher than the other from left to right and from the back of the house down to the fence. I'd like to level this out. Thinking bring the highest part down 10cm and raise the lowest up about 15cm. Not sure how to do this.
Thinking of turning the turf over and adding topsoil to try and get around level then turfing. Would this work? Its Bedfordshire and very clay ground, should I mix with sand & or stone?
I've got about 3x ton bags full of decent soil from where Ive already removed one of the raised beds and a higher pond
Heres a handy dark picture oll get some better ones! Need to get rid of all the gravel area and the circle for new grass

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