Returfing a lawn - how to a raise the height

Hello people, could anyone please give me some advice? I'm wanting to lay a new lawn but would like it to be raised about 3" higher than our current one. My plan is to frame the lawn with new sleepers, and have the lawn slightly higher than the borders. It's a small lawn only 25m2.
What I'm looking for advice on is what to use to raise the lawn, what do I ask for in soil terms and how much is it likely to cost? I'm new to gardening although I have laid a lawn in the past (but never tried to increase it's height).
Also by doing this would it mean we would be unable to use the lawn for a greater period of time, until it beds down?

 

a good silty loam should do it.

raising it by 4cm will be about 1 cubic meter of soil - shop around