Concrete floor grinding and levelling

We have had to move all the new flooring in our house as we found out that the concrete floor underneath is not level. We were due to get the floor self levelled but when the guy doing it look at the concrete he said it needs to be grinded down in some parts. He said from the highest point in the sitting room compared to the hall there is a 25mm difference. I need somebody who has done this before and knows what they are doing to grind down the floor so it is ready to self level. I have been told that the hall, WC and most of the kitchen is ok so it will be mainly the sitting and dining room with a few small areas in the kitchen and utility room