It depends what your budget is. There are plenty of budget-friendly (mostly Chinese) 125s - but these do lack the quality you'll get if you spend a bit more. For example, the Lexmoto Viper 125 (kit.honestjohn.co.uk/reviews/review-lexmoto-viper-.../) and Lexmoto ZSX-F 125 can both be found second-hand for under £2000. The Yamaha YBR 125 and Honda CBF125 are also first bike favourites and definitely worth a look (they're both very popular on riding school fleets). They're very similar (cheap, reliable, basic), but the YBR is more of a workhorse, while the CBF is a touch more stylish and powerful. The Yamaha MT-125 is also a decent option, though more expensive than others in this list.

If you want a 125 race-rep then something like the Aprilia RS4 125 might fit the bill. There are a few used models kicking about for £2500 - £3000. You might also see a few Honda XL125V Varadero on offer, the models from 2008/2009 are often below £2k. A lot of new riders like 125s because they're light and small, but the Varadero will give you a taste of a bigger bike if that's what you're looking for. The KTM 125 Duke isn't a cheap option, nor are there that many on the used market yet, but it's definitely got a lot more character than most of the naked 125s out there: kit.honestjohn.co.uk/reviews/review-ktm-125-duke/

Just make sure you check all the relevant parts on a used bike before you part with any money. Worn chain and hooked sprockets are a bad sign. Check the wheels too, heavily scratched rims can be a sign of frequent tyre changes – which are common on race bikes. Ensure you get both sets of keys too.