If you want the whole lawn to be a little higher, try covering the current grass with thick dark plastic to kill it off over winter then level out with added soil and turf on top. However, if you need it all to be the same average level, removing the old turf manually is the only option.

Wouldn't fancy the latter myself! Besides the hard work, the cost of getting a skip in to dump the old turf may be high if you have no room to rot it down at home.

Looking at lawn grass seed prices, turfing isn't that much more costly these days. It's quicker, too.