An alternative is to see what's available on the used market. Here in the US, it's pretty easy to find a used audio/video receiver or stereo receiver for under $100. Not sure what the used market would be like for you. You might want to ask at
AVForums as they are a UK based home audio/video community. Most likely they would know where to look for deals on used equipment.
Home audio subs almost always have an adjustable low pass filter. So you set the that low pass to somewhere around where the speakers roll off in bass. Some more expensive subwoofers have left and right RCA inputs and outputs, with a high pass filter on the RCA out. My sub has an 80hz analog high pass filter for the RCA out, and so then I set the adjustable low pass filter to 80hz as well. There is some advantage to using a crossover above the speaker rolloff like this as speakers tend to have more distortion in bass at and below their tuning point. If you have a good sub, then best sound will come from letting the sub take over before that point is reached.
BTW: One advantage of AVRs if you can find a used one is that they typically have some kind of bass management system, with more modern ones allowing you to choose from a range of crossover points for the speakers and the sub.