If the exposed wires will drop down to the hieght of the other outlets I think I would cut a 2x3 3/4 hole at outlet hieght,cut another above cabinets if there is no soffit or in the upper part of the upper cabinet if there is a soffit,drop a wire down,put in two remodel outlet boxes and end up with an outlet at top of cabinet. Then you have a connection for your pucks to plug into.Puck light wires can usually be dropped down between cabinets. Many other light options will work with that set-up.

I’m in the same situation, not wanting to put outlets and switches on my quartzite slab backsplash. Today I placed an order for Legrand Adorne components from Lighting and Locks. Before ordering, I sent a drawing to Legrand and they designed the system for me, complete with a shopping list and installation instructions. Lighting and Locks had the best prices and apparently they have 13% discount every weekend and 11% during the week. The light bars were out of stock, so I still need to order them along with one switch. My kitchen is about 8’ x 14’ L-shaped. The total cost of materials will be around $1200. A little pricey but my backsplash is going to look awesome and I’ll have plenty of light and outlets.

@Karenmo I commented above and suggested the Task Lighting for a smaller profile but deleted my above comment and am re-posting here because I think much of what I previously wrote especially about Legrand Adorne being expensive in the extreme was incorrect. I am close to making a decision for undercabinet lighting and outlets for my own renovation, and since I last wrote, I visited a lighting store that had a couple of Adorne pieces in stock that I was able to handle and measure, and I was also given a price quote that I felt was reasonable. It is the control box that is the largest part of this system, and it would hang down below essentially any cabinetry, which you can get a feel for in advertising photos. The angled power bar is about half the height of the control box and would need an under-cabinet lip of about 2" in height in order to be hid, but it's best to check the specs for sure if you were doing custom cabinetry. Since you are installing power bars into pre-existing cabinetry, you would want to make sure that the angled power bar, given its size, would be able to be mounted in some way to meet your satisfaction. For 2 control boxes, 2 power strips, and 2 lighting plug-ins, my total would have been around $500 USD before tax. I've seen posts with people paying up to $3,000 USD for Adorne systems for a large kitchen plus butler's pantry, for example, but we only need the system underneath 2 wall cabinets, so this seems reasonable to me, especially for the nice light control boxes with dimmers included. Sounds like you are just wanting outlets only and not lighting at this point, correct? If that is the case, then many people do a simple plugmold strip. You could easily mount that on an angle, and it would be even smaller than the Task Lighting low-profile units. Thanks for the information about none of Task Lighting's power bars being GFCI. I think we have GFCI breakers to meet the qualification, but I'll double-check. Also, most kitchen appliances wouldn't exceed 15 amp, so you're probably fine with that if you end up with no other solutions. There is discussion in other threads about plugs sometimes falling out of angled strips, so mounting a plugmold straight against the wall would help with the tension on plugs if you ever had a problem with that, just something to keep in mind. Also, I think that in most jurisdictions in the United States, the maximum amount above the countertop that undercabinet outlets may be mounted is 20" (higher than a previous poster stated), but it appears you are in the UK, so your regulations may be entirely different.

This must be regional, because here, all of the lighting circuits are sepatate from the outlet circuits. And are 14 gauge. The trucks are full of both 12 and 14. You wouldn’t have any electrician run a lighting circuit from an 12 gauge outlet circuit. And no inspector would approve a 20 amp kitchen circuit supplying any lighting circuit. It wouldn’t pass the overcurrent requirement. They'd grab from one of the 15 amp lighting circuits. My 70’s house is run that way, as is 90% of any of the houses from then up. Older than that, or with DIY involvement, all bets are off. Its much more organized, predictable, and better design, than higgeldy piggeldy half the house’s outlets and 1/4 of the lights are out.