If the offspring's account has earned more than £100 in interest in a year (so completely unlikely!), then you're required to include it as your own income. The follow on point from that is that you as a tax payer would only have to pay tax on the interest you've received from savings if the interest exceeds £1,000 if you're a basic rate tax payer, or £500 if you're higher rate. If your taxable income is below £16,850 then in fact you can earn up to £5,000 worth of interest tax free.
The bank/building society should provide an annual statement showing the interest actually paid for the tax year. If it's added say 12th April 2016, then that's interest for the 16/17 tax year.