I used a BritRail pass about 5 years ago on a two week trip to the UK which was planned to include a lot of rail travel. Flew into Glasgow and out of Gatwick, and covered a lot of ground in trains. Edinburgh, York, Penzance, London, Brighton - plus day trips. I crunched the numbers when planning the trip. And yes of course, the total price of advance purchase tickets for my various journeys, when compared to the cost of the BritRail (senior 1st class) pass, was much less. But, the cost of those fares as same day purchases was clearly more than the cost of the pass.
If I were a by-the-schedule type of traveler, I'd just buy all advance fare tix, and turn up for all the specific trains I'd booked for (come what may), and it would be a no-brainer that the BritRail pass would be a waste of money.
But I'm not that kind of traveler. I crafted an itinerary in advance and reserved lodgings accordingly, but when on the ground in the UK I tweaked my plans a bit because of among other things, weather and discovering some places I wanted to see. I didn't lose any money on rail fares even with last minute changes of plan, thanks to the BritRail pass. As Toni said above, the big advantage of the pass is the flexibility. I benefitted financially from having the pass, as otherwise I'd have paid same-day walk up fares for a couple of long journeys.
Only you know what is more valuable to you - saving money by buying advance fare tickets which lock you into specific trains, or the flexibility of one of those rail passes. I hope you have a fun trip!