I believe as I am the copyright holder this would be OK, even if there is no model release, right? Or would I have to make them sign a model release so I could use the photos of them on my site?
Regardless of what you can get away with under your local laws and the terms of your contract, why would you use those photos against your client's wishes? As a photographer, you should have no shortage of good images to use in promoting yourself, but paying customers are a little harder to find. There are all kinds of reasons that clients might not want their photos appearing in public, e.g.:
The local office likes you but doesn't want to be obvious about the fact that they're working with a photographer not approved by headquarters.
The photos you took are part of a product launch, and they don't want that information made public before they're ready.
Your images of a fancy corporate party might not send the wrong message to customers, clients, suppliers, or investors.
They actually didn't enjoy working with you as much as you think they did, and they'd prefer not to be portrayed as endorsing you.
I'd like to make a blog article and use some of the photos with some kind of backstory (did photo session with company xy, we had great fun (I hope so :-) ) and here are some examples, followed by some of the photos.
If they really did enjoy working with you, and if there's no reason they might object to making some of the photos public, then why not ask before using them? If they say yes, then great -- you've got your blog post. If they say no and you accept that decision graciously, then they'll appreciate the fact that you respected their wishes. You look good either way, and the only thing you stand to lose is a blog post that you haven't even written yet.
In the future you could discuss the possibility of your using some photos ahead of time, possibly even taking some shots specifically for that purpose. That'd give them the ability to agree to your request, but at the same time making sure that the photos that you might use are okay for public distribution.
I know you were probably looking for an answer based on the legality of the situation, but it really seems to me that building a strong relationship with your clients and giving them the courtesy of approval will put you in a much better position in every way.