I've looked at the pictures and I am quite amazed!!!!. I've never seen this before and I've worked on a few rooves [retired] with Redland 49's interlocking tiles which I'm sure that's what they are.
However before getting the gap closed first go to your local planning office with the photo of the gap [3rd posted] and ask if there is any reason for this gap.
If your findinga at the planning office say it should not be there then close the gap.
If you look at tiles on the right hand side of the gap they've been cut the edge that receives the next tile has been cut off. If your ok on a roof, which I assume you are if you took the pictures, then take off one of the cut tiles on the right and one full tile from the left and try fitting the full tile on the right and lock it's left edge under the tile next row up and see if it closes the gap. bear in mind there is no support batten across the gap. If it fits then join them count the rows up and add 5 to the total number [tiles required] you've got two broken ones to replace which might be the cause of the leak.
My guess at the moment is 'Cowboys' who couldn't tile to save their lives, but I might be wrong, they had one working from the left and one from the right came to the middle and hey presto a gap. How do we fill this we can't move the rows they're nailed. So it seems a trip to
Wickes while the others were sawing off the battens crossing the gap. At Wicks the cowboy spots the corrogated bitumen sheet and thinks 'An Ideal bodge coming up'............. and it's back to your roof nail in the corrogated sheet bodge done. Because IF this was a proper job and that gap has to be there, although don't know why, that gap would comprise what is called a 'hidden gutter' in grade 6 lead and it has to be done properly with timber risers left and right to support the gutter upstand and on the rafters an under support board all the way to the ridge closing under the ridge tile. Or even made as a narrow 'valley'
And from the decription of removing the muck from the rafters says to me in big letters 'COWBOY'S' pity the Indians didn't get them.
Did you have this roof and dormer done ? If done by previous owner then you might have a case against the firm who surveyed it on your and or building society's behalf and should have picked this up.