They are all available on line (I could point you to the Scottish ones that are probably the same)
There is a set minimum and maximum rise and going for each stair, and a minimum and maximum angle. There's also a minimum width depending how many rooms it serves.
i would have thought that the topmost full kit that has been cut down and then butted up to the 'new additional tread' would constitute a hazard. it also looks a bit 'odd' that you were originally allowed a kite riser as a first step.
Im kinda stuck as i cant alter the existing stairs (ones with the kites). There will be a landing of somesort before you enter the new room. That`s if i can get the stairs to work!
Can you not ring or call in to your LABC office and ask to see someone for advice. I am not sure if all, but, some offices do offer free advice on general building queries?
Convert that first corner into a proper half landing, i.e a big square platform.
Then re form the flight leading off into both rooms as a short run of 2 or 3 straight stairs.
At the new room, you need a certain amount of "landing" before the door into the room, so you will have to create a recess for that taking a bite out of the room.
Try not to alter the main part of the stair otherwise that will have to meed current regs re headroom etc so try and keep all alterations to the top bit.