The best illuminated vanity mirror is not necessarily the brightest or the one with the most LEDs. It is the mirror that shows your face evenly from your normal seated position and fits the space you have.
Products and current UK buying options

Product information is researched rather than based on hands on testing. For a named product, confirm the selected model and variation; category links show a changing selection of results.
Get the position right first
Think about where your face sits when you apply makeup or skincare. A mirror placed too far back on a deep dressing table can make close work awkward, while a broad base may take up space needed for brushes and bottles.
Measure the actual usable reflection area as well as the overall frame. A large quoted dimension can include substantial surrounding housing.
Lighting quality beats LED count
A headline number of LEDs does not explain how evenly your face will be lit. The placement of the lights, the ability to dim them and a choice of light tones are more useful considerations.
If you apply makeup indoors but spend the day in natural light, adjustable colour temperature can help you check the result in more than one setting. It is still sensible to look at your makeup in daylight before leaving.
Desktop, rechargeable or mains powered?
A mains powered mirror can be convenient in a permanent dressing area, provided the cable can reach a socket safely. A rechargeable mirror gives more freedom to move it, but you need to consider battery life and charging access. Small travel mirrors trade viewing area for portability.
Check that the stand stays stable when tilted. Magnification can help with detailed work, although it is not essential for everyone.
Where to start shopping
The FASCINATE mirror pictured below is an example already featured in SLUK's comparison of named lighted mirrors. The Amazon link here browses illuminated vanity mirrors generally, rather than promising that the photographed model is the one you will see first.
For a dedicated makeup station, prioritise stability and even lighting. For travel or a small bathroom, compact storage and power arrangements may matter more.