Every DSLR currently marketed will be a noticeable improvement over your current body. Normally a body upgrade isn't significant (the exception being that going to full-frame bodies from a crop-frame body usually provides a noticeable jump in the ability to shoot at higher ISO with lower noise, but even "entry" level full-frame bodies are expensive. A 6D "body only" is just a bit over £1300). But as the 350D is a very old body, everything on the market will be a noticeable upgrade.
While there are lots of nice feature upgrades (e.g. the T5i has a capacitive touch-screen articulating display), if you ignore all the "nice to have" features and just look at the images, the new bodies provide much better handling at high ISO and still keeping the noise levels low. They also have improved focusing systems. Video is built-in to everything (I never shoot video -- so for a lot of people that's nothing to rave about.)
A new Canon body will still be compatible with your existing lenses (with the caveat that *some* older 3rd party lenses may not work correctly. This is rare, but 3rd parties "reverse engineer" the camera interface and they perform testing using only the cameras available on the market. So if a future camera model comes out using a part of the body/lens interface that the third party has never tested, the lens wouldn't know how to handle that. But if this does happen, some third parties can either re-chip or re-flash lens firmware to work correctly again.)
I'm just checking prices at places like Amazon UK and I see that a "new" 700D body & EF-S 18-55mm f/3.5-5.6 IS STM" kit lens is £389. Oddly... if the "body" only version of the same camera costs ... £8 more expensive (you may as well get the new "kit" lens since it's got better optics, faster & quieter focusing, and better image stabilization then the version that would have come with your current camera.)
A "refurbished" body will usually save quite a nice chunk of change but the Canon line site doesn't list refurbished bodies in the UK... they link to a
eBay store in the UK for refurbished products and that store doesn't list any products for sale... at all (did they actually run out of everything due to heavy holiday shopping? Or do they no longer list refurbished products via their
eBay store.) Anyway, here in the US, for example, a "new" 700D (which is called a "Rebel T5i" over here) is $649, but the "refurbished" version is $399 (about £265).