The first LED strip
data sheet says 3.6 watt per foot, the
screwfix transformer
@RandomGrinch has linked to is high frequency AC and you want DC plus needs a load of 35 watt minimum so you would need to use at least 10 foot plus use a rectifier.
Buying as a package is far better with all included. Personally I got Lidi Smart LED Light Strip which has warm and cool plus 16 million colours, it can be set between 3 and 22 watt output and I use in display cabinet at lowest setting, it is flexible 2 meters long can be cut an joined but the joiner provided is very short. It also needs a zigbee controller.
I also tried Ikea and they are rigid, no where near as bright, and expensive for what they are. The manual control means to change from one display to another I have to stand on a chair and press a button, on the colour changing one, and no real option for white.
The warm and cool white settings on the Lidi unit are two independent LED's, and the control allows you to vary the output of the LED's but in a way that the total power does not exceed 2 amp, (22 watt) there are 6 connections I would assume return, cool, warm, red, green, blue but I simply plugged it in and used it, in the kitchen it goes around in a circle under the cupboards to light the counter top,
there was enough space to hide the power supply and controller.
I wish now both sides of cooker were the same, but need to wait for Lidi to do them again.
Over the years I have used many methods to light items on display, from a bulb to fluorescent strip light to LED, all different, and the way the LED lights reflect in glass and beaten metal is rather unpredictable, I have some glass shelves but most are wood, Ikea display cabinets, and so 17 shelves to light, this works out rather expensive with a light per shelf, so I have run the LED strip down the centre so the Lidi one lights 6 shelves and two ikea 3 shelves each, still work in progress, the problem is each shelve is different and I would have preferred to have same lighting on each.
The kitchen strip is held with large cable clips which were pushed in rather than hammered using a pair of water pump pliers. Sticky back does not last I have found.
Each home is different, my living room has one central light, which even with an 8 bulb chandelier is not bright enough for such a big room, so we use the display lights to supplement the rooms lighting. Together with up-lighters etc. So really you have to select and decide what you want. Upstairs I have colour changing GU10 spot lights, as have access to ceiling through the loft, every room and every house is different.
