How do I buy my first car in the UK?

I am living in the UK for the last 8 months and plan to live here for a few more years.

Due to my lack of long term address history, I have not been able to get a car financed or a loan for the same. Nobody is entertaining my short history of stay here even after a steady income flow in the bank account. I have tried a couple of garages and they’ve said the same thing refusing to finance the car.

The car I was looking at was the Mazda 3, 2020reg and I was happy to pay ~ £250pm for PCP. But that model and car was priced around £13k which I will not be able to afford to pay from my pocket.

What is the alternative? How can I have a car to drive to work or groceries etc? Also, any particular suggestions or specific recommendations are welcome for which one to buy starting out which will not break the bank but not give me trouble with maintenance or service frequently.

Thanks!