As per this GOV.UK document, it seems that the answer is no, unless you sold assets worth more than 4 times the allowance, so £50,000 in the 2019-2020 tax year:
You do not have to pay tax if your total taxable gains are under your
Capital Gains Tax allowance.
You still need to report your gains in your tax return if both of the
- the total amount you sold the assets for was more than 4 times your allowance
- you’re registered for Self Assessment
Then, as per this other GOV.UK document, losses needn't be reported right away:
You do not have to report losses straight away - you can claim up to 4 years after the end of the tax year that you disposed of the asset.