Unless over the weekend you will give whatever car you buy a good run out (decent acceleration through the gears up to 60/70 for a reasonable time/variety of roads, not just more jig-jog on local roads with a trip to the supermarket/shopping centre), then for such low mileage, forget performance cars (Golf GTis included) and diesels.

Smaller, petrol-engined town cars would be far more suitable (those you quoted are ok, but could you stand using the next size down [Hyundai i10/Fiat 500/Ford Ka etc]) if you realistically only needed it for commuting/weekly shop. The 'warm' versions of some of them can still be quite peppy to drive as well as reasonably frugal. I suspect though, with the sort of budget you're looking at, you'd better look at the older, more basic cars - less to go wrong, and, for those running a car on a budget, less to insure and maintain. You also get a newer car for the money.

Your type of driving actually lends itself to buying a hybrid, but they aren't cheap and I wouldn't buy an older one, mainly because of the expense of repairs/battery replacements that may occur (if you could even find one in your price bracket that worked ok) at that age (over 10 years old).

Recommendation: something small, Japanese/Korean, petrol-engined, only the essential gizmos (to keep the price down), and a proven full main dealer service history/MOT passes/all issues fixed. Ask to see the log-book and proper invoices/receipts for all maintenance and reapir work.

If you think it looks didgy or the seller is reluctant to/won't show you proof of the above, the WALK AWAY - there's lot of other decent cars out there. Take you time, and bring along a car-savvy (the oily/electric bits) friend/family member/breakdown staff (a good investment) if you are looking outside of a franchised dealer network. Don't be pressurised into buying the first car that meets your needs - look at a range at different places.

For 80 miles a week, get yourself down to Halfords and buy a Boardman road bike and some suitable cycling gear, paniers and lights.

And don't forget a good helmet - I'd suggest Giro as they are designed and made to US standards which are considerably higher then Euro ones.

On those few days a year when it really is too inclement to cycle, get a taxi.

Despite what some other posters on here have put, your usage is quite normal for city dwellers. By the time you've added weekend and evening mileage in you'll be at about 8000 miles per year

If this is your only car, I'd recommend something Golf or Astra sized so it is comfortable enough for longer trips away. For 5k you can get a 3 year old Astra (1.4 petrol), and in SRI trim you get the Golf GTi type looks without the hassle or cost of a performance car. Obviously it's no where near as quick, but plenty quick enough in town or on the motorway.

If this is a second car which is just being used to go to work and back, there are three options.

1) Buy a car for a few hundred quid, use it until it breaks and then buy another one. (This often works out very cheap indeed - a mate bought and kept a £350 car running for three years once with just petrol and the occasional oil change.

2) A nearly new petrol version of any of the current crop of city cars. My favorites are the Skoda Citygo or a Fiat Panda, and keep it for years.

3) Get one of the above or similar brand new on one of those £100 per month finance /leasing deals (which always limit mileage to about 6000 per year) and keep in the new car cycle and will cost you £1200 per year for the privrlege . This option is least likely to have extra cost from repairs and servicing, you might even last the three years on the original set of tyres!

That's the best of reasons to go off-topic, Focussed. Your Dad's generation lived through a lot, and we often forget the reserves of courage shown by firemen. He chose his car well too: his Minor no doubt started easily on a wet morning, whereas if he'd had a Ford Anglia he'd have got there sooner on the bike.

I strongly agree with the suggestions above of the 1.3 Toyota Yaris. If it's too small for you, Mr ?, the Corolla/Auris would do just as well.