Repair of antique standing lamp light fitting (UK)

It is great to begin woodworking with a custom made project that fits your needs. Often doing it yourself can result in a significant savings, but I think you may find that purchasing the components for the lamp may well cost more than the amount they are asking. But your version will be the size and finish you want.

For the linen panels, you could try mounting the linen on thin plastic, such as acrylic, cut to size. You could use spray adhesive, such as this one, or you could tension the cloth and glue the edges with a thin bead of a general adhesive. Just make sure it will stick to the type of plastic you select and do a small test to make sure it does not discolor the fabric.

Screw length should be enough to go through the first piece and 1/2 to 2/3 of the way through the second. You need to pre-drill all holes. Glue will stabilize the piece.

Finally, be sure to leave the top of the lamp open to allow heat to escape, and be careful when stapling over wire not to nick the insulation. You should consider attaching the wire with a bead of glue along the length instead. You can hold it in place with tape until it dries.

The easiest way to run an LED off of 120VAC is to use an LED that's already designed for 120VAC, like a 120VAC LED Panel light. They come in a wide variety of sizes, colors, and form factors.

(Photos from Digikey's catalog).

Just keep in mind that 120VAC is dangerous, and if you're not actually going to panel mount them where only the front of the LED is exposed to the user with the rest of the LED shielded by an insulating or grounded panel, make sure that you keep them safely isolated so the user can't inadvertently come into contact with the back side of the LED housing or wires.