Yes and no. Your employer is allowed to monitor your use of the internet at work. They can do this with or without your consent, but only if they tell staff clearly in advance what is being monitored. Employers are likely to be monitoring, for example, how much time is spent on the internet and what sites are being visited. Check your company's internet usage policy to see what the situation is where you work. Some employers routinely block access to social media sites like Facebook at work.
Monitoring the extent of your usage is not the same as policing the content of your Facebook page – unless, of course, you have invited your manager to be a Friend on Facebook.
If your employer is especially concerned about Facebook use, the best advice is never to mention your work on Facebook, and to be very careful who your Facebook Friends are. Most tribunal cases result from a co-worker or manager printing off a Facebook entry they object to and sending it to HR.
The law does not regard social media sites as 'private' spaces, no matter how few in number your Friends are. This means it is unlikely to be a breach of privacy for your employer to look at your Facebook account, unless they have hacked into it.
The best advice is not to identify your employer on Facebook at all.