17,000 miles a year implies lots of motorway and dual carriageway driving. Why specify petrol? Diesel will work just as well if not better and in the current climate, you may pick up a cheap one because people have been scared into avoiding them.

Sounds like a job for a typical Focus/Golf size car with a 2.0 turbodiesel.

I suppose it really depends upon both how well looked after a £4k (and likely 5-7yo) diesel-engined car was, and how it was driven during its previous ownership - the former may be relatively easy to find out via electronic records from the dealership/manufacturer (assuming its bought from one) and the DVLA MOT results site, but the latter definitely isn't, even if the mileage appears to be genuine via MOT test results, as two or more years or low annual mileage could mean either lots of short trips to the shops/school OR less numbers of longerjourneys (not anywhere near as bad for the DPF etc).

The history would, in my view, be a LOT less trustworthy if much of it were NOT electronically held (not sure what happens if you get a car serviced at an indie, especially a 'back alley' one, however proficient they are at the work itself) or absent if done by an indie or an owner themselves.

As SLO says, older (and more complex) diesel engined cars that have all the three-lettered acronymn emissions components, etc are a potential financial disaster in-waiting UNLESS you can guarantee the entire maintenance and running history of the car. It can be similar (though lower risk) for petrol-engined cars, but as he says, certain ones are far more hardy than others and also attract owners who treat these cars more sympathetically as per the manufacturer's guidance.

That's not to say the OP may still find a good'un diesel, but the likelihood is lower and the risks (£££ and breakdowns) higher, even factoring in the difference in fuel costs for an above average annual mileage (though below most people's nominal changove point of 20-25k miles pa). I suppose it may well depend upon the OP's ability to tell the difference between a good and not so good car (especially if they look cosmetically very similar) or willingness to take a likely higher risk, particularly if they have limited funds for any major repair/replacement.