Replaced the radiator and retested and told me unfortunately the head gasket had gone

I was driving around town and I received a message from the on board computer saying the coolant was over heating. Fortunately my home was just around the corner, so I parked the car. After allowing the car to cool I checked the coolant and it seemed a little low, so I topped it up. Next day I drove to work and back and everything was fine - about 3 miles. The next day I did the same journey, this time the message came as I arrived at work. When I checked outside the car water was squirting out of the radiator. I had only stopped for a short while and made a decision to drive back home in the over heated state (bad decision I know), but I thought 3 miles? Anyway BMW replaced the radiator and retested and told me unfortunately the gasget had gone. MY DILEMMA - They can't tell me if replacing the gasget will be sufficient to resolve the problem. They said the engine may be warpped. Do I give it a go or replace the whole engine? At £1600 and £4000 respectively. Or give it up as a loss and buy a new car. I know the current value of working model is around £5k. I have done 25k miles in this car and it has done well until this point. Plus it was a great drive!