Car appreciation... the aesthetics, the engineering, etc

Depends on your definition of 'little' but cheapest lease deal I could find with a quick google works out around £7400 over 5 years (Fiat 500). £5k will get you a 4-yr old, very low mileage, FSH model. That gives you £2400 in service/mot costs before you're worse off and you still have a useable car at the end of it, which will be worth more than not having any car at all.

I worked it out with a similar budget (wanting an estate/larger car) and even over 3 years I'm saving enough to pay for the quite expensive first service bill and still be miles away from lease costs.
As an aside, my 2007 reg car appears to be worth approximately what I paid for it (possibly more!) 18 months ago. Clearly not sustainable in the long run but shows that depreciation isn't linear.

Both my wife's and my car are leased. How good 'value' they are depends a bit on what metric you use to measure 'value'. I was pretty flexible with the actual cars we got in exchange for getting good deals (general consensus being that total lease cost over a 2 yr lease being anything less than 23-25% of the RRP for the vehicle is a good deal).

For both cars I am paying less than the depreciation over the 2 year period which feels like good value to me but that is of course using the cost of a brand new car as the bench mark.

An interesting point of reference given your budget - total lease cost (6+23 months) of my wife's Volvo V90 is £7,830 on a car with a sticker price of just under £38k. I had to settle for not picking my own spec as a Volvo dealer up north had the vehicle on site and was offering it at this price as I suspect he was under pressure to move it.

Having said all that, the lease market is pretty crap for buyers (leasers) right now though, very few deals about.