Would not say these are ultra-cheap. There is probably a lot of "price that the market can sustain" going on here, rather than what it costs them to build the cars
But those aren't the sub-$10k ones, right?
I don't know if they sell the exact same model (same range, same speed, same tech trim etc) for $10k but I would not be that surprised that they'd be making a huge huge outrageous profit just because they can in the UK, because that is what the competitors are charging so why not?
FWIW there are cheaper things on sale in the UK but they are much lower spec. E.g. £15K OTR gets you a 45bhp (yes, 45!) Dacia Spring that will get you from 0 to 60 in 19s (19!!!) and only go 100 miles between charges. Suddenly that BYD dolphin looks amazing. There is the Citroen AMI for £7.5k OTR, but that is legally not even classified as a car (it's a "quadricycle") has a range of 46 miles, a top speed of 28mph, and has not been crash tested by EuroNCAP ... It would likely be a total shit show if it were though. The BYD looks like a decent option by comparison, but I'd personally not pick one because they are such an unknown in this country and the price needs to be even lower for me to take a punt :)
At least they have 5 stars in the Euro NCAP assessment: https://cdn.euroncap.com/media/82666/euroncap-2023-byd-dolph...
And they're being sold in Mexico in N. America, for 358,800 pesos (1), which is $18,000!
(1) https://mexico.as.com/motor/byd-dolphin-mini-que-tiene-de-es...
Some countries like Denmark etc. have very high sales/registration taxes (then again EVs were mostly exempt from them for quite a while, and maybe still are?). In most other countries you only need to pay VAT (~20%) but then there are various rebates/subsidies which might fully offset that (especially for cheap models like this)
European spec BYDs tend to have 5-star (max) crash ratings.