If you're on the 6.55am or 8.55am - forget it, BA aren't selling many seats in business so won't offer you a promotional upgrade. If you're on the 1.15pm or 9pm you should view your booking in BA.com's Manage My Booking page and see if there is an "Upgrade Special Offer" displayed prominently at the top of the page and on the far right of the page (doesn't always show, it's a bit of a lottery), which would let you pay cash for an upgrade. Failing that, as mentioned above you can ask at Heathrow check-in if they have an "Upgrade Promotion" on your flight