Roof advice wanted, please

The gable end of my house looks like this...

By that I mean that
1. The slates lap directly onto the bricks, there's no edging of any type, no overhang.
2. It's a mess.
I want to know what that type of edge is called if there is a name for it, or even, what do you call the 'bit where the roof meets the wall'?
And is it possible to get some sort of cover for it? I've seen a sort of plastic angled thing that goes over tiles but not one for slates. I've got a scaffolding tower and I'm capable of pointing it, just wondered if there were other options.
Ta.

By that I mean that
1. The slates lap directly onto the bricks, there's no edging of any type, no overhang.
2. It's a mess.
I want to know what that type of edge is called if there is a name for it, or even, what do you call the 'bit where the roof meets the wall'?
And is it possible to get some sort of cover for it? I've seen a sort of plastic angled thing that goes over tiles but not one for slates. I've got a scaffolding tower and I'm capable of pointing it, just wondered if there were other options.
Ta.
The older I get, the better I was.
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Maybe using traditional mortar would be an easier option (and cheaper). A temporary wooden batten on the wall and a bead of mortar (use sharp sand) would neaten it up.
I'm sure there must be a roofer on here.
Where the fcuk is that supposed to drain to? Is it literally just flat from the gable end?
Pinnacle Monzonite
Part of the anti-growth coalition
Edit - I'm in the east, in the rain shadow of the southern uplands (mountains as nice as the Pennines that you haven't heard of and that I don't want you to visit, fcuk off) so we get about 7-800 mm a year on average. London gets nearly 700, on average.
https://www.roofingsuperstore.co.uk/product/dv9-dry-fix-continuous-grp-face-fix-dry-verge-for-scottish-slate-3m.html
It is a DIY job if you are ok with heights and have scaffolding, do not do it off a ladder. The products are very slate/tile specific so worth taking time to research exactly what you need. The plastic cover(s) essentially fix on to the wooden battens that your slates are nailed to. It's a bit fiddly but easy enough - sturdy access is the key and a DIYers knowledge and handling of tools.
You could redo the mortar, I suppose, but you'd probably end up redoing it quite frequently. Dry system is pretty much maintenance free.
Bianchi Impulso
BMC Teammachine
“When I see an adult on a bicycle, I do not despair for the future of the human race. “ ~H.G. Wells
Edit - "Unless it's a BMX"
Pinnacle Monzonite
Part of the anti-growth coalition
The house was built in 1911, so it hasn't done too badly, but I suppose it has been pointed before when the brickwork was done.
I'm not too bad with heights, as long as I feel safe, hence the scaffold tower.
The older I get, the better I was.
It's not a brilliant design, but it's not something you look at really is it? "oh, it's got the right number of bedrooms, a great location and massive garden, but just look at the way the slates join the gable end"
Actually, the buying process didn't go anything like that.
I'm living in the house i was born in, literally, I was born in the bedroom where I now sleep each night. I moved out when I was around 20, to MY first house, later got married and then moved to another place. When my dad died, it got too much for my mum, and so we bought it off her and she moved to a bungalow.
It has a lot of memories. If I take old paper off the walls, i find things underneath that I drew as a kid. I upgraded a radiator, and the marks for the fixings behind the old one are the those i made when I hung it at about 13.
The older I get, the better I was.
House purchases tend to be heart over head. Ours was.
We have a highly flawed roof that turned out to put the tiles lower than the gully next to the skews and sealed with mortar. So had the tendency to funnel water under the mortar and down the inside wall, rather than a faster drainage route down a gulley.
We now have a lot of lead to seal it.
Don't talk to me about the electrics.
Pinnacle Monzonite
Part of the anti-growth coalition
He put about 5 loops of fuse wire around the oven fuse. You could have run hs2 through it. And then there was the extesion plug inside the wall, in the bathroom, under the leaking pipes. And the live nail in the skirting board.
The garden wiring was much worse though.
Pinnacle Monzonite
Part of the anti-growth coalition
You wont catch me on the roof though....
Yes dry-verge. or no-more-nails to hold a length of UPVC angle onto it. REally the edge should be slightly raised compared with the rest of tiled surface to encourage the run off down the roof rather than off of the edge. I'll wager the the wood is rotten on the so lifted the tiles off of the mortar joint.
True story. The daughter was a lifelong friend of my wife's. Except it was a badly wired dishwasher, that had just been installed by a kitchen company and she was electrocuted by it.
(I'm not arguing about what exactly was changed, but know it was to put a stop to anybody doing it who wasn't qualified).
Pinnacle Monzonite
Part of the anti-growth coalition
In my experience both of these are perfectly acceptable ways to wire a plug or a light fitting or a wall socket.
Not even sure things need to be earthed these days.
I tried to wire up a washing machine motor that way once.
I'm okay now.