With all due respect, if you'd read the terms and conditions of the BAEC website before signing up for your free 100K miles, you'd have already been prepared for this.

That said, there are many ways around paying BA's hefty fuel surcharge. Use 40K miles (plus $75) to fly to Easter Island on LAN with stopovers in Santiago and Lima. Use 50K miles to fly to Bali on Cathay Pacific with a stopover in Hong Kong.

These miles are extremely useful if redeemed carefully.