Back wheel - bearings worn out. Replaceable. May also need trueing. Routine fix.
That's good, but only if the hard plating isn't worn out. I bet the cones are shagged and wouldn't be surprised if the cups were too. I doubt it uses "sealed" bearings, which would be fantastice because you could replace them.
The trouble with us lot saying to replace the worn out parts is that for us who do it ourselves, it's a doddle. But if you are new to it all and have to learn every step of the way, it's a very big jump. Even worse if you can't do simple stuff like mend a puncture. Just going into a shop and buying a new bike that will work is very attractive.
It's a matter of what you want.
£150 for a new bike is a very low price. I reckon that to get the equivelent quality of car brand new, you'd have to spend 20 times that amount. A £150 bike would be like a £3000 brand new car.
I don't know if you could buy one for that price*, but it would be at the absolute bottom end of the market. Would you trust it?
But buy a £3000 second hand car, you'd get something pretty good.
*and that's the point really. You might get a serviceable bike that will last a few years, but probably not as long as your old bike. But most likely, you'll end up with something more akin to a child's toy that will be worse than the bike you have within a couple of years at the very best. Probably a few months, even weeks.
Every part of a bicycle will wear out in time and it's always cheaper to replace bits as they go. I know people who have had the same bike for 50 years. It's just made up of totally different parts to what it originally was.