In a nutshell, the answer to your question is YES your wife can work.

Switzerland has signed a lot of agreements with the EU (and is part of Schengen) which means that for employed nationals from EU/EFTA states, the Agreement on the Free Movement of Persons applies leading to a straightforward permit process not subject to quotas.

Any non-Swiss national who works in Switzerland for longer than three months requires a permit.

Workers receive a G permit (Cross-border commuter) if they are EU/EFTA residents (which is the case for your wife) and work in Switzerland. They may stay in Switzerland, but must return abroad at least once a week and register their Swiss residence with the communal authorities (for most of the EU nationals that rule does not apply as they have a full freedom of movement).

As you see the small difference applies between nationals and residents of the EU.

But in you case, the most important is the following:
Family members of EU/EFTA employed nationals are granted an EU/EFTA permit even if they are non-EU/EFTA nationals but live permanently in an EU/EFTA country. The validity of the permit is limited to the duration of the main holder's position. Family members may work, but must notify the cantonal authorities before doing so.

For more information:

The Federal Office for Migration regulates the conditions under which people can enter Switzerland in order to live and work there. You will find more on their website.

You will find the contact details of the various Cantonal Migration Offices on the Swiss Confederation website.

Last but not least: read our guide for expatriates in Geneva, with an article on visa and permits in Switzerland.

 

You're welcome, we're here to help
On family reunion you will find the "official" information here (French)

Although, on the down-side, I have just remembered that the UK is not part of Schengen, so Schengen agreement does not apply, but as this is a member of the EU rules do still apply.