In a word, yes.
Most UK companies will have a clause in their contract with you which says something about "bringing the company into disrepute". That is, if you go around saying "my boss is an idiot and our products are rubbish" they are entitled to start disciplinary proceedings against you.
Many companies now have a "Social Media Policy" - that will explain what they do and don't want you doing on social media. For example, you may not be allowed to call yourself "Bob_myworkplace" or make out that you represent the company in an official capacity.
They'll also say that you can't share confidential information in public.
Now - there is a limit to this. If you have a totally private Facebook account and post "crap day I work, I hate my boss Fred" - then they're unlikely to find out.
If you say the same thing in public, you can expect a reprimand.
Similarly, if you see someone ranting about your employer - don't comment. That's not your job.
The flip side is - what happens if you say "I'm gay" on Facebook. Can they fire you for that? No. But if you say "I want to hit all the kids in the daycare"... well, what do you think?
I would ask your boss for a copy of the firm's social media guidelines / policy. It may also be worth asking for training so that people don't inadvertently fall foul of the rules.
As ever, if you're currently facing disciplinary proceedings, it's worth talking to your Union Rep - or a specialised employment lawyer.