I believe it's on the entire trip if it is on one booking reference. However, unless you booked the trip aggggeeeeessss ago then I don't think it will make a huge difference (if you are only changing date) as I don't think there has been much of a change in the taxes in the last 6-8 months. I had changed the date of a LH trip booked in the first half of last year only a couple of weeks ago and the tax changes were a couple of £ (and that was at the destination rather than LHR as the departure point).

You could try doing a dummy booking and see what the taxes are?