Paul, I can give you the technical answer, at least in part, but my experience is almost completely in North America and whatever part of the UK you're in may have standardized color code and codified wiring requirements that I'm not aware of. I know that home alarm system peripherals are generally wired differently ( a bit more complicated) in the UK/Europe than in North America. We tend not to wire most homes as if they were jewelry stores.
You need to find the other end of that 4-wire cable and see how it's hooked up at its siren driver (may be called something else in the UK?), a PCB module that takes a DC input and modulates its output to produce the warble on the speaker. Here in the USA, we usually tuck the siren driver in the control panel cabinet, but technically it can go anywhere on the sounder loop between the control panel and speaker.
If I knew the model of your control panel (not the keypad), I could tell you what wires to trace from the CP to find the siren driver, but it may be obvious when you look in the CP cabinet. The siren driver will have a DC input where polarity must be observed, and an output where polarity doesn't matter. The output is modulated AC.
You'll probably find the wires paired at the driver output connections, so you'll know how to pair them at the speaker.
Disclaimer: All alarm systems, by their nature, are customized.
Not knowing what other components are in your system, or the layout of your home, I can only guess and may need more information if this doesn't help right away. A control panel model number and a clear picture of the stuff inside of your control panel cabinet might be helpful.
EDIT: Drat, almost forgot: Some alarm control panels have built-in siren drivers. Took me a minute to remember that because the industry in the USA has gotten away from that in the last couple of decades. It may still be commonplace in the UK for all I know, and there may not be a separate siren driver module. That's why knowing the model number of your control panel is important.
If the driver is integral to the panel, you should find some clue in the labeling of the wire terminals on the control panel.