Realistically you are talking £1.0K for this trip. I had a few days in Calvi at the end of the trip before the flight home, these costs have been included but the overall cost could be reduced by camping where I stayed in hotels or if you don't have any time to fill before your flight home.

Getting there

Return flights Newcastle to Calvi (via Amsterdam and Marseilles) £545.00
Hotel in Marseilles £103.21
My share of the taxi from Calvi airport to Calenzana20 EU£16.46
Food shopping in Calenzana37 EU£30.45
Freeze dried food taken to help keep food weight down £34.50
6 nts camp fees @ 7 EU per night42 EU£34.57
Meal at Refuge L'Onda20 EU£16.46

The end of the walk & getting home

Meal at Vizzavona14 EU£11.52
1 night accommodation with Evening Meal and Breakfast @ Vizzavona72 EU£59.26
Train to Calvi19 EU£15.64

Depending on how long you have  to wait for your flight home and the type of accommodation you use in Calvi, the costs can vary a lot. Here's what I did:

Hotel in Calvi, 2 nts125 EU£102.88
Moderate subsistence for two days120 EU£98.76
Taxi to the Airport30 EU£24.69
Grand Total