Is this lack of petrol?

I am at the girlfriend's house in Wales. Drove the car yesterday and the low fuel light came on yesterday. Drove about 10 miles with it like that and parked it. It snowed last night and the car was covered in snow. The car park is steep and I parked facing downhill. Today we wanted to go out so I cleared all the snow from the car then started it. Started first time, engine ran for about a minute then died. I started it again, started first time again, ran for a short time then spluttered then died. I tried again, started first time again, I tried revving it to keep it from dying but it died. The next subsequent cranks it doesn't start (has it used all the available petrol? ) as though it is getting no fuel. Battery is fine as it is cranking fine. No miss fire either. Fuel gauge is on zero mark and fuel light is on. Is parking on this steep slope facing downwards starving the fuel pump pick up? I can hear the fuel pump prime when I turn the key to position II so the pump is ok. Strange one this. Nearest petrol station is 30 minutes walk away and all girlfriend's friends that drive are not answering their phones, typical. I hope it is low petrol as all my tools are back at home in Bristol. I will get some petrol tomorrow as it is raining now. Any ideas what the problem might be?

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