Dual tax agreement

Your personal tax allowance is still valid in the EEA

We have a house in Brittany and plan to retire there when my husband is 65 in January 2020. He has a UK army pension which will be taxed in the UK under the dual tax agreement with France but will he still have his tax-free allowance (we may rent out our house in England and I read in a recent Connexion that rental income is taxable in the UK after personal tax allowance)? S.H.