Rule 1 is never spend anything which you would not spend if it is not later reimbursed. Unless you either have a prepaid card or a commitment entered in the PNR notes (not likely), you will always face the prospect that BA won't reimburse for this or that.

Given BA's generous cabin allowances, it always makes sense to have at least the first 2-3 days clothing with you. Even if your bags are delayed only by a few hours, nobody wants to spend their day shopping after a long trip.