I've already described making the lighting pelmet, which was then painted along with the layout itself. A little secret, I've already described the lights too. Last year I got a strip of "Natural White" (4000K) LEDs to experiment with, with this embryonic layout in mind. However in the event it was my son's micro layout Slugworth that got to use them first. That did show the lighting was very effective and a good colour balance, and only used 1m of the 5m length, so I had plenty left for Hexworthy.
The strip is self-adhesive and can be cut at the marks every 3 LED's. Easy enough, but it didn't stay stuck to the ply even though it is painted, and even after a layer of PVA was tried first. The solution was to spread contact adhesive over the wood, then when it was tacky stick the self-adhesive strip to it. So far that seems firm enough.
The "holy grail" of lighting a "cameo" shelf layout like Hexworthy is even lighting, including right to the front of the layout. It's difficult because we want the lighting neatly tucked out of sight in the pelmet, but really it needs to be high up and well out front - where the viewer is. LED strips are good at distributing light with minimal shadows but putting them right over the models only lights them from above. I chose to add the main strip towards the back of the pelmet bar, putting it about 2" or 3" back over the layout facing down, then a second strip split between the front fascia facing backwards, and the underside of the beam facing downwards but right at the front of the layout. Hopefully this puts plenty of light at the front. Ideally the strips would be at an angle facing the layout, but I couldn't find an easy way to do this. A hot glue-gun was used to cover the ends of the strips, securing them and protecting the soldered joins, and also to secure any loose wires.
The view of the whole beam shows the arrangement of strips, plus the foil I pushed into the front edge to hopefully reflect and diffuse any stray light. The strips were joined by soldered wires, taking care to match the "+" and "-" marked on the strips (I hadn't thought of this when sticking the strips down so some are the other way round, not a problem as the wires can be crossed provided polarity is matched), and joined by a terminal block at one end. I added 5.5x2.1mm DC connectors to both ends of the pelmet - because it might be useful being able to plug the power in at either end - and bought cheaply as a pack of 10 pairs I might as well use them! These connectors have screw terminals but no way to secure the socket in place, so a big lump of hot glue is used, along with a couple of screws so they can't pull away.
As there is more lighting than Slugworth I thought Hexworthy needed a bigger power supply. The LED's use about 1A per meter, not knowing how many meters I'd use I went large and got a 6A supply - plenty as it happens, but I'd rather know it isn't overloaded. It wasn't expensive, and a sealed plug-and-play unit is convenient. I was disappointed to find it fitted with a 13A fuse though (the mains side is rated at 1.5A), I've swapped for a 5A for now as that's the smallest I had in, but will find a smaller fuse.
All plugged in, and we have light.
In situ in the dining room, and with the building in place, the light is bright - actually, maybe a bit too bright. There is a reasonable amount of light reaching the front of trains on the station track, even with the lighting bar in the flush position, though as expected moving the lighting bar forward really helps with light on trains on the front siding. I don't think any further light will be needed at the back of the layout.
When I bought the light strip I also got a dimmer switch, being ridiculously cheap and thinking it might come in useful. The easiest way to try it seemed to be to attach in-line plug and sockets, and fit between power supply and lighting.
It's not easy to illustrate the difference with a photo, which exposes for the amount of light, but it does allow the light to be dimmed without affecting the distribution or colour of the light. Incidentally it doesn't dim all the way to off, but switches off from a low brightness. The dimmer allows the light to be adjusted to the light in the room, but I may yet experiment with just dimming the rear strip while keeping the front strips brighter.