Diesel is more expensive per litre than petrol. This means the mileage necessary to justify a diesel is pretty high.

Usually considered to be around 15k per annum. If the OP is doing 350 miles per week, that would be around 18k. If the petrol averages 50mpg and the diesel 60mpg, the difference in the diesel's favour isn't that big. If the but if the petrol is using super unleaded and the diesel averages 65mpg, it is around £550 per year.

You need to take account of the cost difference of petrol and diesel at the moment as well - it's generlaly 20p a litre more for diesel and at the moment I don't see it getting close to the price of petrol anytime soon.

I'd say that the 15,000 mile minimum is really only for someone buying new and using predominantly for longer journeys that avoid DPF active regens (to avoid the DPF/oil starvation-turbo/oil dilution problems).

I'd personall agree with what I recall HJ himeself saying a good few years ago, that for second hand cars, that figure (under 'normal' fuel price times) would be much nearer to 25,000 miles pa.

At the moment, the difference in price between petrol and diesel is higher in percentage terms than it historically has been, perhaps caused by the Western embargo on Russian natual gas and general electricity shortages (some people in rural areas using disel generators to heat/light mones and businesses) and a big increase in the number and usage of diesel-engined home delivery vehicles in Western nations.

Given the above, if I were the OP, I'd consider getting a modern petrol supermini or Focus-sized car, because they are generally (with some notable exceptions) amongst the most reliable (staying away from dual clutch and some CVT ones for the most part), long-lasting cars (mechanically-speaking), but are far more fuel efficient that 10-15 years ago, getting much nearer the manufacturers' claimed mpg than diesel-powered cars do.

I'd personally go for something in that Focus size (not necessarily a Focus, e.g. not the 1L turbo, especially the DCT gearbox version) given the OP has a family (useful for holidays/days out for size) and something registerd just before March 2017 to get as new as possible but taking full advantage of the better VED bands (those well under £100pa) compared to the £150+ for anything afterwards that wasn't an EV.

I'd also get something that has a full service history (main dealer throughout preferred) and that obviously has been well treated, as well as being the minimum spec (the least gadgets that could go wrong or aren't actually a must have) required by them. This means a mid-lower spec car, shod on sensible wheels and tyres (which will also save a lot over the longer term) and with less to go wrong. It would also cost less to insure.

This means they could afford cars from makes that are considered best for reliability and/or may even leave some change after buying it if they are lucky.

Given second hand car prices are likely to fall in the coming months due to the inevitable big recession, getting as much of a car in terms of value (which isn't the trim level but what it'll cost you over the coming years, which build quality/reliability plays a big role) is more important than raw mpg, even with fuel prices being well above historial levels.