Yes, you have to submit an income declaration to French tax authorities each year for the previous French tax year (the same as the calendar year).
Taxation of income is done in the country in which you reside, not the country from which the income comes, with the exception of property and “government” pension income, which is always taxed in the country from which it comes.
You can still rectify this if you have not been doing it. Usually, the tax authorities only go back three years, so you could submit declarations for 2016, 2017 and 2018 income.
Then you would redo your HMRC tax returns for 2015/16 (from January 1, 2016), 2016/17, 2017/18 and 2018/19, only showing income from property rentals and “government” pension income, which is income from the military, police, civil service, diplomatic service and the like, essentially (but not exclusively) that which is paid by the Paymaster General.
All other income, such as state and private or work pensions, interest, dividends, National Savings income and so on, is declarable and taxable in France.
You will then have French tax to pay within 30 days of receiving the French income tax assessments, but your UK tax refunds may take longer.
Tax overpayments confirmed by HMRC that are made in the current tax year are refunded through the PAYE system, but all tax refunds due from previous tax years are refunded by cheque by HMRC directly.
Get the advice you need with our Income Tax in France 2020 Help Guide
Primarily aimed at Britons living in France or those in the UK receiving income from France (such as from renting out a holiday home here), our help guide details the information needed to make your declaration. It shows how to declare income such as pensions, rent, ISAs, shares, savings and interest, and includes a visual guide to the French forms.
Reader's query answered by Hugh MacDonald
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