Saving interests pushing you up to the higher tax bracket

Let's say you earn 50k annually after pension contributions. That puts you just below the basic tax rate giving you 1k personal saving allowances.

What happens if your saving accounts interest goes above 1.2k, let's say 1.5k thus pushing you total income to the higher tax bracket. Does that create a paradox where instead of just paying the 40% tax on the additional £300 interest you earned, you now have to pay 40% tax on £800 interest because your personal saving allowances have been dropped to £500?