Make good floor after chimney breast removal

[Soph&Edd]

We have removed the chimney breast from our bungalow (full chimney, breast and stack removed) down to the concrete floor. There is some brick remaining that we have had to chip away at - but we've stopped as unsure how deep these bricks will go! My question is how do we make this area level with the rest of the concrete floor? The floor in the whole house is concrete and we plan to remove and replace the LVT in this room at some point, so want it to be ready for when we do that. Also wondering if there is any need to think about damp in this area - will it have been damp proofed below the chimney breast? Thanks in advance