Currently use QGISCloud Pro and looking at alternative options to this.
We are wanting maps to be hosted on the Web to allow users with specific access rights to access them.
We have already looked into ESRI.
Software Recommendations Stack Exchange is a question and answer site for people seeking specific software recommendations. It only takes a minute to sign up.Sign up to join this community
Other commercial options would be
From an open source perspective, this article here below was quite good and relatively current. Albeit written in context of migrating from Mapbox GL, so the solutions listed below are basically open source libraries (ie: They may not offer a hosting solution, you would provide that yourself).
Maptiler is open source (but not free?) and OpenmapTiles offer hosting solutions and are open source.
Take a look at the UMN Mapserver, which was very popular for WebGIS Projects in the 2000s, but it is still around as free software. It has a PHP 7 API which you can combine with the rich set of tools for user-management, authentication and authorization that several PHP frameworks provide, e.g. Symfony