Don't glyphosate it. You will be left with a rooty mess. You need to strip off the turf (slice it into rectangles with a half moon then lift with a spade) then dig over the whole lot. Rake the soil level, firm down, rake again to a fine tilth then seed or lay new turf.
We did in our old house, but it was just the lawn. The rest of the garden we had dug things up, including an old air raid shelter, and brambles. We did rotavate the lot both front and back gardens. Where the lawn had been we covered with good quality membrane and then pea shingle at the back. In the front we did the same but added loads of compost as we had clay soil and then planted stuff through the membrane, all the plants grew really well.
Thanks for the advice re glyphosate- that was Plan A!
Someone also said that once you remove the turf (using a turf cutter), don't rotovate as you won't end up with a fine, level surface. They added just fine sand to level, then a thin layer of topsoil, then the new turf, so you'd need to chop down enough to add all that stuff or your new lawn might be too high.
You could rotavate, but after that you would need to do further works to make sure you had an even surface and fine tilth for seed sowing. Rotavating would be like digging: it would make the soil less compacted allowing air and water to move through it more quickly, but wouldn't give you a fine crubmbly flat, level surface.