The first example you posted is probably as good an example as you are going to find, but it is a lot of money. When I look at £4500, I'm thinking you could be well into mark 2 Jazzes at that price.
You are going to pay more from a dealer, there's no way around that, but I would expect there to be quite a bit of negotiating leeway on that price, especially at this time of year. If you can go without a part exchange, that will help you too. One problem with dealers is that they generally want to sell you finance, as it is quite lucrative for them. If you are a cash buyer, it severely limits the profit they can make from you.
I wouldn't get too hung up about the low miles, particularly as you are intending to do less than average mileage anyway. Hondas will stand the mileage, and you would never guess the mileage on a high-miler - the interior on ours is testament to that. Personally, I would always go for newer car with average miles, rather than an older, low mileage car at the same money. They all deteriorate with age.
Check out similar cars on Gumtree or auction sites, to give you an idea of the spread of private and dealer prices.