As nmc980 said, it'd hardly be feasible given the number of miles you would require and cost of the miles. It'd make more sense to check the cost of changing your flight to business, you can do it online for the entire leg (LHR/LGW-BNE) or ask at the check-in desk about upgrading just one of them.
Change fee is waived for upgrade to higher class of travel, so only fare difference applies