You can work this out by trial and error or algebraically.
If you have no savings, you currently pay £7250 interest and receive no interest from savings. You would pay £8000 under the new scheme plus the £150 fee. Stick with the current scheme.
If you have £30,000 in savings, you currently pay £7250 and receive £1500 interest on your savings (a net payment of £5750). You would pay interest on £70,000 under the new scheme (£5600) plus a fee of £150 (total of £5750). Same as current scheme.
If you have £50,000 in savings, you currently pay £7250 and receive £2500 interest on your savings (a net payment of £4750). You would pay interest on £50,000 under the new scheme (£4000) and pay £150 fee (£4150). Go for the new scheme.
Alternatively, 7250 - 0.05x = 0.08 (100,000 - x) +150 to get x = 30,000.