From what I'm reading you need bridges for specific devices, unless they support Z-Wave or Zigbee (may well be wrong on this...).
In general, you need a "bridge" for everything - including Z-Wave and ZigBee. A bridge may be as simple as a USB dongle and some software, or it may be a stand-alone box, but there must be something to handle the radio and protocol interface.
I'd prefer to use Zigbee devices but it seems very much still in development.
ZigBee is a mature and well development system, although it may or may not be commonly used in different parts of the world. ZigBee has been around for 15+ years, and ZigBee 3.0 has been released for a few years now. Of course new features continue to be added, so in this respect it is still in development.
ZigBee is used quite extensively in commercial systems (lighting and Smart Metering) and possibly the most well known implementation are the Philips Hue lights which use ZigBee Light Link (ZLL). Other systems by Osram and Ikea (among others) also utilise ZLL so are compatible.
Is this not available in the UK?
ZigBee is available in the UK, but is not particularly common for home automation where Z-Wave is more popular. It is used extensively in Smart Meters, and many lighting products use ZigBee (ZigBee Light Link profile is now merged into ZigBee 3.0).
There are USB dongles available in Europe, and unlike ZWave, ZigBee uses the global 2.4 GHz band, so a ZigBee controller or device bought anywhere in the world will work find in the UK.
There is an open source ZigBee stack here, and you can find a list of controllers on this page. This stack is used by openHAB and a number of other commercial and open source systems.
If a device supports Zigbee, providing a binding etc exists in the home automation software, should it work? As in, a Zigbee controller doesn't only work with certain devices? That's more the software?
I'm not sure I understand this question. A ZigBee device must contain a ZigBee radio and protocol stack to work, so a ZigBee controller will only work with ZigBee devices. ZigBee defines a (so called) ZigBee Cluster Library which defines a common way for devices to interact, so as long as devices implement standard ZCL commands, then it allows ZigBee devices from different manufacturers to communicate with each other.
The ZigBee Alliance performs certification to ensure that devices correctly implement the ZCL commands to ensure that they will be compatible. Any device that uses the ZigBee logo and name should have been certified by the Alliance before being placed on the market. It is worth noting that there are devices on the market that are not certified even if they may partly follow the ZigBee protocol, and therefore may not work 100% with devices from other manufacturers (eg the Chinese Xiaomi devices).
I hope this helps cover your questions.