In the U.S., the type of lights you're looking for are often found hanging above workbenches in the garage or basement, and are sometimes known as "shop" lights because they're in the workshop. You buy them at Home Depot or a hardware store, not a specialist lighting shop or Amazon.
"T5" as a designation covers a number of lengths of light bulbs and fixtures. The Amazon link is to a specialized tiny 12" (300 cm) long bulb for a special reading lamp or home fixture, such as an under-cabinet kitchen light to brighten a kitchen counter work space.
The Sylvania Luxline is yet another dimension, this one 1.5 meters long. This type of bulb is generally installed directly into an overhead fixture, and controlled by a wall switch. It's an office, basement, or store ceiling light bulb.
What you want, if you're shopping for T5 fixtures, is the larger 21 inch bulbs and fixtures.
This, for example, emits 1000 lumens so you'd put four of them into a four-tube T5 fixture.
Or you can look for what are known as high-output T5s, which put out more lumens.
In the U.S., the standard workbench light is the T8, which is four feet long. The main reason to use T5 fixtures is due to space considerations, as they're only two feet long. However, since T5s aren't as ubiquitous, they tend to be more expensive.
I'd encourage you to check out Home Depot, hardware stores and other places that sell worklights, and get familiar with what's available locally. Sometimes online isn't always the best shopping.
I think that part of your online shopping problem may be that you're evidently searching for light bulbs, not light fixtures. Try looking for the fixtures, and then find the bulbs or tubes to go in them.
But ideally I'm looking for lights that are 50-60cm long to fit under a shelf.
That would be the T5s, but the ones that are 21 inches or 53 cm long.
You're looking for something like this. Two tubes, 4000 lumens, high output.
They will need space to hang, they are not installed directly to the shelf above the plant shelf.
So does that mean that a 500 lumen light actually gives out more or less "lumens" of light depending on how close you are to the light?
A fact of physics is that, the further from the light source you go, the dimmer the light. The amount of light that comes from a light source diminishes in proportion to the distance from the light.
NASA has math, if you're into it.
https://www.nasa.gov/audience/foreducators/9-12/features/F_How_Far_How_Faint.html
So at the level of growing seedlings under lights, decreasing the distance between the light source and the seedlings makes a measurable difference.
I have lights in my basement, and I move them up and down according to what everyone needs, brighter or dimmer.
Part of my setup.
These are the big T8 fluorescent shop lights, hanging on chains from a PVC frame that rests on an old door.
I give each type the light they need by moving them according to the lights. The orchids in the back need bright light, so they're directly under the back fixture.
The purplie Tradescantia in the right foreground needs rather less, so it's kind of in between the fixtures.
In the main foreground there's a black tray of annual flower seedlings to go outside eventually. When they started, they had the fixture right down on top of them, 2" from the tubes. But now they're bigger, the lights are up more
And in the rear there are two snake plants, who don't need the direct light and get along find in the reflected ambient light at the end of the tubes.
So these placements all reflect the way that light rays travel and diminish with distance.
Maybe I underestimated just how much light plants need and just how expensive it is to provide all that light artificially!
It's an initial expense, but the upkeep is no more expensive than running more lamps in your house.
£250 grow light
Right. So you don't buy a £250 grow light from a specialist, you go down to Home Depot and get a work light.
In the U.S., the ubiquitous T8 four foot long fluorescent shop light costs around $20-30 USD for the fixture, with maybe $6 USD for each of the two tubes that are required.
because if it's the only artificial light option
It's not. I've got a whole basement of plants that says so. :D