Is there a way to make a browser aware of iBeacon devices in its proximity?
Similar to the way HTML5 Geolocation is working...
If not would this be something that can be achieved with a browser plug-in that can provide the detail to be consumed by javascript?
This looks promising (2016), Google Chrome developers site showing a desktop browser feature as a work in progress.
https://developers.google.com/web/updates/2015/07/interact-with-ble-devices-on-the-web?hl=en
https://github.com/WebBluetoothCG/web-bluetooth/blob/gh-pages/implementation-status.md
Unfortunately, no. No web browsers have implemented any bridges between beacon detection and JavaScript.
I don't think a plugin approach is possible on mobile browsers (either iOS or Android), because neither browser supports asynchronous communication between external apps and JavaScript in Mobile Safari / Mobile Chrome. The best you could do is have a custom app that responds to a beacon, then launches a web page in the browser. But I realize that isn't what you are asking for.
If you want to build a native app with JavaScript, you can use Cordova (aka PhoneGap) and use plugins that provide beacon support. My company has one for our ProximityKit beacon framework:
https://github.com/RadiusNetworks/proximitykit-plugin-cordova
There is also a Cordova plugin that has basic beacon support here:
https://github.com/petermetz/cordova-plugin-ibeacon
There's a W3C specification for this Web Bluetooth, but there's no support yet: http://caniuse.com/#search=bluetooth.
If you decide to write a Phonegap plugin implementing this spec will be a good starting point.