I’m not sure if UK terminology is different, but in the US we talk about an engine thermostat being either OPEN or CLOSED. I assume yours was stuck closed, which will cause overheating. I don’t know of any way to get one “open” other than breaking out its center, jamming something into it, or removing it. All of those require accessing/removing the thermostat, and I wonder why a new wasn’t put in then, as all of the work to do so would have been done.
Anyway, to your question–it’s not likely to do significant harm in the short term, but it can cause problems if left that way too long. The engine will not reach operating temperature. The expected results of that are warm instead of hot air from the heater and increased fuel consumption (because the electronic control system perceives the engine as still being in warm-up mode). Some of the excess fuel can get into the oil and contaminate it.
So you won’t ruin your engine in couple of weeks, but it would be wise to do the repair as soon as you can, and to have the oil changed once it’s done.