[UK] Do I need to report to HMRC if I earn less than £1,000 (personal savings allowance (PSA) basic rate taxpayer) in interest? I also have CGT of less than £12,000.
No, if you aren't doing anything complicated. The intention is to get basic things like PAYE and interest from banks and building societies filed electronically, rather than you having to manually let them know by filing a tax form.
In fact, even if you earn more than the PSA, they don't really want you to file taxes because they know anyway.
"You need to register for Self Assessment if your income from savings and investments is over £10,000." https://www.gov.uk/apply-tax-free-interest-on-savings