It's a smallish cut on the sidewall, and I don't think it goes deep enough to reach the cords. Thanks.
If you can't see or feel the cords by lifting the edge of the cut with a blunt instrument (e.g. a coffee stirrer), then it shouldn't fail:
any ply or cord that can be seen without touching the tyre – fail
if by folding back rubber or opening a cut with a blunt instrument, so as not to cause further damage, exposed ply or cord can be seen irrespective of the size of the cut – fail
if a cut which is more than 25mm or 10% of the section width whichever is the greater, is opened with a blunt instrument and cords can be felt but not seen – fail
Source: UK MOT manual
However I'd still seriously think about replacing it, as it will have seriously weakened the sidewall, significantly increasing the risk of a blow-out.
This question's answer How to assess the severity of a cut on a tyre sidewall probably best answers your question. I am blocked from accessing the link as outside the UK - relevant part of the testers' manual.
I think @Nick-C's advice applies to the tread, not the sidewall.
What I can tell you is that in (litigious) North America, most tire shops would refuse to even attempt to repair.
Tires cut or punctured in the shoulder or sidewall areas, as well as any tires driven on while flat or with very low inflation pressure even for short periods of time are often damaged beyond repair and should be replaced. Driving on a tire while flat or with very low inflation pressure will permanently weaken the tire's internal structure, rendering it more susceptible to catastrophic failure.
But on the sidewall, those cords aren’t there. So, there’s just no way for a plug to fill that hole. The patch won’t hold, and it’s going to continue to leak.
In fact, I took in a tire that had a small ( < 0.5") screw still stuck in the side and they would not even touch it. Maybe they were trying to see me a new tire, but why would you risk a blowout?
Also, that's not a "smallish cut"; that's severe and has clearly compromised the integrity of the sidewall.
btw: every time you go over a bump in the road, the stress is transferred/absorbed via the sidewall first, which makes it more stressed than a patch on the tread.
I'm an mot tester. The mot standard is the minimum requirement to be Road worthy just because you have an mot and it passes doesn't mean nothing will happen within 12 months till the next mot. That tyre will only fail if there are cords exposed or ply! Or if the vehicle examiner thinks that the cut is deep enough to reach the ply or cords, on the view of the picture I would advise would need the car and tyre in front of me to give a better judgment. My advise is to change the tyre anyway before the mot safety reasons thanks.