The term 'subwoofer' can cause a bit of confusion. Folk have this idea that subwoofer automatically equates to T-Rex stomping about in Jurassic Park. It can, but that required much larger drivers (cones), much bigger boxes, and a heck of a lot more power than your typical sound bar can muster.
How come a sound bar can claim to have built-in subwoofers then?
The answer is that subwoofer frequencies start much higher than many realise. Try 200Hz.
That number might not mean much, but go to YouTube and type in '200Hz test tone'. I'll bet you can hear that from the dinky speakers of a laptop or even your smart phone. It's a much higher pitch than you'd associate with subwoofers. That's why little sound bars can make the claim.
Where does this leave us with external subs then?
200Hz is the top of the subwoofer frequency range, but it goes way way below that.
In theory, music gets down to 20Hz because that's the limit of our hearing. In practice, stuff playing at below 30Hz is already getting hard to hear. At 20Hz the chances are you'll only feel the sound, not hear it. Sub bass for movies (the LFE track) can get down to 3Hz. You'll need some serious gear to push air at that frequency, but it's all in the sub range and way below what any sound bar can attempt.
The subs in a small sound bar will be starting to tail off significantly at 60-70Hz. If you hear much below that it'll mostly be the higher harmonics that accompany each fundamental note. Adding a decent external sub will help fill in what's missing, and depending on how good tou are at blending the two, you'll also be able to flesh out a little higher to add weight to the bars lower frequencies.
Your budget will determine how successful you'll be here.
Budget subs are not thin on the ground, but there's a lot of stuff out there that's not really worth the time. As a general rule I'd steer away from Eltax, Boston, Q Acoustics, Yamaha, Auna, Cambridge Audio, and anything made by any firm that produces TVs. A 10" driver and around 150W of power is a reasonable starting point for a smallish room for 2-3 adults. Bigger rooms require a bigger sub and more power.
Best bang for your Buck is generally BK, some KEF, some of the larger Tannoy subs, maybe Monitor Audio, B&W, and REL.
BK Gemini II goes for around £90-£150. BK XLS200 is the same 40cm cube but runs with a better driver and more power. I have seen them go as low as £80 and up to £200.
KEF PSW2010 can be had for under £100 used. This has the same infinite adjustment controls for crossover and phase as the BKs which makes it easier to dial in where the sound bar lacks bass management. KEF PSW2500 has the same 10" driver but with more power and a larger enclosure. £80-£150.
That should get you started. Look in member's market here and on eBay and AV forums classifieds.