New lawn wanted, how?

So, we've got a bungalow which has a largish garden 55m X 10m.
Without going on (too much), we have several grass areas, and it has a lot of bumps lumps and scars from old raised beds etc, and the grass doesn't look to healthy, also in the winter the garden got very very boggy as we think the water table is very high near us, when digging in one corner a foot down I almost had standing water!
So I want to have a main "nice" lawn, about 10m X 10m, and also build the ground up so it's higher level and easier to mow and get less boggy!
I would think to raise the whole of this approx area up and turf it then I may cut out areas for planting later once grass is established.
The main problem with doing this is access to our rear garden is by a 1.1m side path, so tonne bags of soil and proper machinery difficult to get in!
How much would this cost, how much work is it, what would I do?
Do I just get a rotivator/digger churn it all up add a couple of tonnes of soil then slap some turf down? I'm quite hands on and not shy of hard work!
Any advice comments very welcome,
Thanks in advance

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