After a deluge of biblical proportions a few days ago, I noticed the guttering was clearly blocked.
The blocked section is just before a 90-degree corner (the inside of an "L") and obviously the crud washed off the roof refuses to go around the corner and therefore quickly blocks it leading to an overflow.
Remedial job of getting up there to clear the crud out is on the workstack for a dry spell.
In the meantime a more permanent solution might be to drop an outlet from the corner so crud can get washed into the drains.
As luck would have it, the corner is where the stench pipe/soil stack I (re) fitted stands. With a AAV on top.
I'm thinking that *if* I can get a piece to fit the (plastic square profile) guttering I could feed it through a U-bend into a boss on the stench pipe.