Are you referring to the two-week quarantine imposed by the government over which the employee has no say?

Yes, they have no say in taking the quarantine. But they do have the choice of where to take their holiday. I don't think it is acceptable to ask an employee for 4 weeks' absence on such a short contract. There's conflicting rights and expectations here.

Can the work they would be doing be postponed? Why not just have them make up for the two weeks afterwards?

I take it work for home is not an option in this case?

@Bennet it's not clear from your question, or from responses you've written under the answers below, if you are prepared to 'give' anything at all in this situation other than the 2 weeks of time off previously agreed to. So, to be blunt, are you expecting your employee to foot the entire cost (not just financial) for the situation you're both in, or are you prepared to contribute anything at all to offset this? I'm assuming that at the time you agreed to the 2-week holiday to Europe that neither you nor the employee were aware of any quarantine - this is a surprise event on you both.

Was the holiday booked before the government quarantine was announced? I think this is relevant here.

How far in the future is the holiday? If it's not in the next month or two, chances are the quarantine will be lifted by then.

Can they work from during the quarantine period? Many of us are working remotely (from home) during the lockdown period until the office reopens.

Is this a contractor or an actual employee with a time-limited contract?

Thinking out loud... I'm assuming the reason they can't WFH (stated in the Q: "no remote work arrangements") is that it's some kind of on-site work like construction project management or that type of thing, and their project can't just be delayed by another 2 weeks as there are other people working on the same project and probably a contractual deadline.

Consider this: The employee goes on their 2 week holiday, and they return to work after the 2 weeks because you said "no" to the government enforced quarantine, then it turns out that the employee did contract COVID while away and everyone gets sick and has to take 2 weeks off. The problem is, if you say "no" to the quarentine, you are also indirectly saying the employee should not take their holiday and you won't pay for any inconvenience that has caused.

You say they need to work on site, could it be that their work falls under one of the exemptions? The "Information technology or telecommunications professionals" in particular.

"Ask the employee to find cover for the 4 weeks themselves?": such a bad sign that this would even cross an employer's mind.

@TymoteuszPaul: of course they do have a say. They know that there is a quarantine, and they decide to take holidays which will force them to go though that quarantaine (assuming they knew it when they were purchasing the tickets). The alternative it to take their vacation in a place where there is no quarantine (which means the UK in that case). This is their say.

That you agreed a two-week holiday and your employee bought tickets seems both clear, and also irrelevant. Of course you would struggle with unpaid quarantine after returning… Your choices would seem to be either to come to an agreement with your employee about sharing the cost, or to persuade your professional association to beg the Government for help. In any case, do you truly believe all those details you Posted above could really matter?

@CaptainEmacs People need emotional/mental resets even MORE in the midst of a global pandemic. I don't see how it's relevant.

If I was in a position to do so, I would offer to split the difference

@corsiKa It's relevant because: if OP booked before the quarantine was in place, they can argue that it was not their fault not knowing that they need to quarantine after the trip. If they booked after it's known that there is a 2-week quarantine, the employer can argue that they should have asked for 4 weeks and then the employer could have said "no" in view of this. What they need or not is not for discussion here - only whether OP informed their employer fairly about how much time they would be away.

@CaptainEmacs I disagree - for whatever reason they didn't ask for this quarantine. Maybe it didn't occur to them. But the truth is this whole pandemic is rather inconvenient for both people and employers. This came up and has to be dealt with. If someone neglected to say this before, like, deal with it the same way you would if the person was in the hospital for that time. And if you're not prepared for that as an employer, well that's really on you, not the employee.

@Bennet , I would suggest to you: "Before starting, we agreed for them to take a 2 week holiday to go home to Europe (no problem here)." that is an incredibly bad idea. If people are working they are working. We never, ever entertain bizarre schemes that "edge" on business travel with "but can I visit my Mom?!" nonsense. I'm afraid it's completely unbusiness like to have ever said "yes" to such a scheme, and unfortunately this is an example of how only chaos can follow when such things are involved.

@Fattie: Could you clarify your comment for me? To me, it seems like you say "it's unbusiness to let somebody visit their family in their holidays" which cannot be what you mean (?)

@Fattie in the UK at least (and surely in most places) it is illegal to not give your employees a minimal holiday allowance. Like it or not, 8 months' employment contract entails some holidays (and that's fine by me, for the most part...)