Nothing wrong with a secondhand DSLR and it will (probably) take better photos than a £100 point and shoot.
I bought both my DSLRs secondhand and had no problems.
You can start off with a 350D (if Canon are your thing) with a kit lens for that price, then save up and add a couple of decent lenses and then in a year upgrade the camera body (keeping the lenses) for a newer Canon body, like a 450D (still secondhand but newer).
Buying decent lenses (these can be secondhand too) is worth the money, because you can keep them for years while you just change camera body to upgrade functions and sensor size. With Canon, you could buy a lens, use it on a 350D and carry on using it even if you upgrade right up to a 7D body.
Not everyone has £500 odd spare to splash and I wouldn't buy a camera on finance.
So yeah, I would spend £150 ish on a s/h DSLR, buy a lens or two over the course of the next year while you learn how to use it, then upgrade the body later. That way you're not spending hundreds of pounds all in one go.
Also with a cheaper s/h camera you won't be as scared about using it, dropping it or taking it out and about.
Bear in mind however that a 350D is quite old now, and it might have been heavily used.
The main problem with DSLRs is that they use a physical shutter, so this only lasts so long and after 20,000 photos it might have had enough. So when looking at s/h cameras, check how many photos it's taken (shutter accuations/operations).
