Hi,
If you are removing chimney breasts on party walls, and leaving the stack on the roof (I would assume you are as they are probably shared) you need more than just an engineer report.
1) Party Wall agreement, you must have this before any work is started. Normally easy to sort out providing you get on with your neighbors, if not can be costly. Should you commence work without it, you will be liable for any damage your neighbor says you have caused!
2) Structual engineers calculations and design for the support required to hold up the chimney stacks.
3) You should inform the council for 2 reasons : 1) they have a record that the correct steels/support was installed and 2) they will check that any support has been installed correctly
I personally would inform the council as if you are planning on selling the house at a later date this may cause problems as there will be no offical record for the support beams used, probably causing you to drop the price just on this alone.
Also when choosing a tradesmen, make sure they know what they are doing as steel beams require padstones, packing etc. Should this be badly done and the council condemned the work, it can be costly to put right.
Also make sure the builder has insurance - a MUST when work like this is being done.
Hope this helps
Rob