Raising the level of the lawn/beds

[83dons]

Hi I have built a summer house with stones around it. My garden slopes from the top where the grass is level with the base of the summer house to the bottom where the lawn is like 6-8 inches or so lower than the base. How would I go about raising the level of the grass and plant beds to the same height. I was hoping to source railways sleepers to lay along the bottom of the garden (there are already some around the summer house) and up the side fence too where the soil beds would meet the fence (as the neighbours garden will be a bit lower than mine). Also lay wooden panels around the beds at the bottom and side. Do I need to buy in some subsoil and proper soil to build up the level on top of the existing grass (which is patchy at best) and then buy rolled turf to lay out on top and more soil to build up the beds? Just looking for the cheapest way possible to do it myself really. Is it likely I can source old railway sleepers from a station maybe? Not sure what sort of volume of subsoil, soil or amount of grass to get hold of. The patch of grass needing replaced will be about 2.5m wide (from summer house stones to bed sideways) and 5.5m long from bottom bed to parallel with front of summer house. There is a photo below. Feel free to ask any questions. Would like to get this done this summer so the grass can take before winter.