Elizabeth,
If the options were granted while he was UK resident, they are supposed to withhold 40%. If the options were granted before he became resident, no tax is withheld.
Assuming they were granted in the US, follow Guya's advice.
Assuming they were granted in the UK, then if they screwed up and gave it to him without withholding the tax, they have to still pay the tax now; which is why they want him to pay now. A nice company would let him pay them back over time; a nasty company won't. Most companies will arrange for small employee loans in emergencies (for example, advances of salary to help an employee through a rough spot). He should arrange for a company loan if he doesn't have the £600 to hand. The company should honour the request as it is their fault that they did not withhold the tax.