First thing I feel at the wheel when front tyres are getting marginal is understeer in the wet on a tight bend like a roundabout.
But the legal limit is really for wet weather braking performance. Anything under 2mm is basically inadequate in an emergency.
Our resident tyre man Jock wrote an interesting article on this not too long ago.
If only getting two new tyres I would advise putting them on the rear. Understeer you can deal with, swapping ends is a different story
Resident tyre man Jock? Fame at last! Many of you will know my thinking on these things and there's lots of sensible comment above. There's two observations I'll make here though and one is that you've no way of knowing the history of a part worn. Some drivers abuse their tyres something rotten and this can significantly weaken it's integrity. I don't want to be the one that finds this out at 70mph in heavy traffic on the M6! So I will never buy a part worn. There used to be a large warehouse not so far away from me which was piled high with part worns. He quoted me a "silly" price to supply and fit the new tyre I was looking for so I took him up on his offer. It was immediately obvious doing new tyres was a novelty for him, there was not one new tyre on his premises that I could see - he did a decent job of fitting it, with the paint "blob" in the right place, but the balance was a bit sketchy and I got it rebalanced after living with it for about a month. Anyway, I had a good look round his stock while he was handling my purchase and was quite surprised to see a goodly number of the tyres were well past the half worn mark. They still looked really good because they had evenly worn treads with, apparently good tread depth, but when just visually inspecting tread depth you need to factored in that the tyre is illegal at 1.6mm (a new tyre will have around 7 to 8 mm, most are around 8mm tread depth) so a tyre with 4mm tread depth is not half worn as it only has 2.5mm useable tread left! Worth mentioning also, that in a series of tests I was involved in many years ago, we found that when tread depth went below around 2mm wet weather performance on a properly wet, but not totally flooded, road surface became very poor. So I try to renew my tyres when the tread is around the 2mm and certainly well before it reaches 1.6mm. With this in mind, if I were to buy a "half worn" tyre, say with 4mm tread depth still on it, I would be actually buying a tyre with only 2mm useable tread! So, as I tend to change my tyres in sets of 2 or 4, so I always have a balanced set across an axle, I will be changing them when the most worn tyre is at this level so the one on the other side of the car may still have half a mil or so before getting down to my self imposed limit. I place safety for self and family - and others - way above the saving made by running the tyres down to 1.6mm though.
The other thing I think is worth thinking about is that the Chinese/far eastern tyre manufacturing plant and technology has moved on massively in recent years. So much so that there are now some surprisingly (to me) good product arriving on our shores these days. Also there are some good quality British brands being manufactured in China and other eastern countries using absolute state of the art factories and processes - For instance Davanti.
https://davanti-tyres.com/about/ to name just one. I think it's important to separate recent production from historic though and I'd be one of the first to say I've had some pretty terrible cheapo tyres in the past which originated in the far east. However, thinking about recent acquisitions, I've had Sumitomo tyres on one of my cars which were as good as any and my boy now has a set of 4 on his Audi A4. They were only fitted a week ago but he's reporting very favourably on them:
https://www.sumitomotires.com/Home/default and the Falkens:
https://www.falkentyre.com/en/company/production-facilities I had on the Ibiza, which I think are manufactured by Sumitomo, were excellent in all respects except I found them a little more noisy on some road surfaces compared to the original fit Bridgestones. What I can't do is advise you on which are worth buying and which to avoid because there are so many different brand names. A big clue might be though that if they are "super cheap" they might be best avoided.