Your speakers are floor standers. They already have reasonable bass extension. £80 isn't really enough to buy a new sub that's worth owning that will add anything useful for music.
The V4's have a quoted frequency range of 32Hz-25kHz. The bass end is 32Hz, but that's a little optimistic for useful bass. 45-50Hz is closer to the mark. A typical budget sub (<£200) isn't going to get much lower than 40Hz of useful bass extension. Those under £100 will have a hard time making useful bass below 50Hz. So, at best, they'll add to the existing frequency range of the V4s rather than providing anything at lower frequencies.
If you're just looking for louder bass without going any deeper then (new) a Tannoy SFX sub at £99 is about your minimum level.
For both more and deeper bass then you'll have to look at used. Maybe a Polk or Wharfedale. They were often heavily discounted to under £200, so the used prices might sneak in under your radar. Search AV Forums classifieds or on Ebay. Also look at better brands (Mordaunt Short, Monitor Audio, Kef, Tannoy, Mission) which were/are often sold as part of 5.1 ssystems but then replaced by higher performance subs.
Edit: There's an AE sub closing out on Ebay shortly. It stands at £79 with no bids. If you live local then this might be a reasonable buy
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