Help Me Buy A Used Car So That I Can Get A Job

After moving to the UK from China, I had an extremely limited budget, so I purchased a 2004 Smart ForTwo with 80,000 miles on the meter and 6 previous owners for £650, after fees. Unfortunately, after I drove it for four months, a bit of spark plug broke off and fell into the engine. I have been informed (by three separate mechanics) that the car is totally unsalvageable unless they rebuild the engine, which will cost between £1,800 and £3,000.

Since I need a vehicle (pretty desperately) in order to secure employment (I am currently interviewing and both jobs I'm being considered for require access to a vehicle as a prerequisite) I have been searching for a suitable used car. I will also need to use the car to take my son to and from school, so safety is a top priority for me.

It's difficult to find a safe vehicle for under £5,000, but I have located several which cost between £3,000 and £5,000. The vehicle that I get will depend on the budget that I manage to secure. I will obviously pay to have it inspected by a third party mechanic before purchasing. I am therefore budgeting for the possibility of having to inspect multiple vehicles.

Further complicating matters, I am only licensed to drive Automatic vehicles and I have neither the funds or the time to take a manual course.

Any help will be tremendously appreciated. I am painfully aware of the fact that there are many more deserving people out there. If you choose to help me, I will be sincerely grateful.

UPDATE

A friend found a 2007 Skoda with 47,000 miles on it and only one previous owner, so this car is now the goal. I've paid a deposit to hold it, and I'm getting it checked out by AA to ensure that it'll last a while. If it passes the inspection, and I can raise the money to purchase it, this is the car I'll buy. I've given it a test drive and I was incredibly impressed with it. Hopefully, with your help, this car will see us through for at least a few years. Thank you all so much, for all of your help.