You will have leaks in no time, and when winter snow builds up, the water will pour in - surely BCO hasn't approved of any initial drawing or the work in-situ?
What did BC say when they did their mandatory roof inspection? Surely it was obvious at that point that you were going to have this problem and it should have been pointed out. Did use an architect? Did he specify this construction? I assume you are building off a notice as opposed to full plan submission as this would surely have been questioned before a spade went in the ground. I wouldn't be happy with this and would want the roof redone properly at the expense of whoever is responsible for this clanger. If this is not possible then you have a couple of options to try to prevent ingress.
The cheapest option would be to address the problem specifically beneath the windows. You already have water pooling on there, this is bad, especially when it freezes and thaws. You must redo this so it incorporates the maximum fall you can achieve. Remove the felt and use finings or wedges to get your fall then board and membrane, flashed properly where possible and whatever you can achieve under the window sill, flashing tape, silicone etc.
you need eaves protection on each of the 'gable ends' around your windows just as you do on the eaves of your extension, you could frame it and use cement board under your tiles for a mortar bed and UPvc cladding at the sides with your membrane flashing under the cladding.
Another option is to do away entirely with the roof where the pitch ends and have it done as a flat roof from that point, membrane, flashing etc.
Replacing your upstairs windows, adding a couple of courses of bricks to raise your sill height is an option...
It's hard to tell how much lap you have on your flashing at your transition but it doesn't appear to be enough, perhaps get this checked?
As I said at the start I wouldn't be happy with any of those options and would have the entire roof redone, the pitch you will be left with may be too shallow for tiles, I don't know, in which case a major rethink is in order.
Also, it might be my eyes but do you have engineering bricks up to dpc?
Hope this helps, I'm sure I've missed a few things but it might point you in the right direction.