Yes, your company has every legal right to control which devices connect to their network. It's a pretty common IT security measure, especially if they handle sensitive information. The corporate network is the company's property, and they can set whatever rules they want about who accesses it and how. It's not unreasonable from a legal standpoint, though I get that it's frustrating for you.
What you can do is formally request that they add your laptop to the list of authorized devices. Usually there's an IT department or systems administration team that handles this. Prepare the information they'll ask for: your machine's serial number, MAC address, model, that kind of thing they typically need. If you work two days a week in the office and need to transfer large files, explain that clearly in your request, noting that mobile data isn't sufficient for your role. Most companies authorize devices that actually need to be connected.
If after making a formal request they keep blocking you without reason, then there could be an issue with discriminatory treatment or breach of your employment terms, but first exhaust the normal process. Sometimes it's just that nobody knew you needed access - not that they're deliberately denying it.