I can't recall now but correct me if I'm wrong isn't Manchester to Wigan something like 10miles apart on the motorway?
I'm guessing you're needing a fairly dependable car due to being involved in the medical profession?
Anyway I'm generally a buyer/user of automatic cars only these days, too damn lazy to shift gears. However I'm also rather picky with my automatics as I don't like being stranded or needing to be in a situation where I need to rescued or ride in a recovery truck
Since you are buying used, the one thing I would do is to buy a car with a very conventional automatic gearbox as buying anything else on a budget is somewhat asking for trouble. Hence I'd avoid any of those cars with a semi-automatic or automated manual transmission as these things are like a timebomb, there are no accurate ways to inspect whether components within it are on their way out or not unless you strip that gearbox, the main thing that does go with them is the electro-hydraulic pump that will go after some time and they do cost a fair bit of money to replace, we are looking at the 6-800quid type money here
The other thing that will go is the actuators and solenoids, this one depends on the car, Alfa Romeo and VAG vehicle ones are expensive while those on a Fiat and Toyota or Honda aren't that bad though you would need to bring it to a transmission specialist that knows these gearboxes in order to fix them, there aren't that many of those around tbh especially in UK.
The Yaris from that era uses a MMT gearbox which essentially is a sequential manual gearbox, it has a clutch which is controlled by a hydraulic motor and an actuator unit that selects the gears for you. It is all controlled by a rather smart ECU. The main problem with it is the ECU does fail, a sure sign that it is a failing one is when you stop the car at a junction it goes into Neutral and then it won't go back into gear again. The other failing point is the hydraulic motor, can go between 2-5 years depending on usage, there is no way to diagnose this as one day it will just completely stop working. This is also one car that you will need to send back to a dealer or a Toyota specialist who has the electronic tools to set the biting point of that clutch every other service or so, otherwise it the clutch will wear out prematurely.... it will be an expensive job to replace the clutch. While the Yaris in itself is a great car, the ones in Europe equipped with the MMT gearbox is a crap car to be avoided, which is why the latest model no longer uses that gearbox.
The Polo at that price you would be looking at later models of the Mk4b versions, these came with the 1.4l 75PS or 84PS (in later models) and a very standard normal automatic gearbox. My parents had one of these (though it was manufactured by VW of China rather than in South Africa like the UK models) It survived the rigours of Beijing and did 43000km in 2 years before it was sold off, never had a single issue with it. It is a reliable car and should suit your needs if all you are after is some wheels with an autobox. The Skoda Fabia is similar under skin with this and the automatic model does behave differently than the Polo version, I'd give it a test drive and you may be able to find one that is newer for the same price.
Other than that, I'd also look into a Suzuki Swift or a Honda Jazz.