Under Article 19 of the UK/Belgium tax treaty here
, if your civil service pension is what is referred to as a "government service" pension, it will remain taxable in the UK as well as in Belgium. It would be taxable in Belgium alone if you were a Belgian national whilst not also being a UK national. The list here
should tell you whether your civil service pension is a government service pension or not. Any UK tax paid on this pension will be deductible from any tax liability you have in Belgium on the same income under Article 23 of the tax treaty.
Your rental income will be taxable in both the UK and Belgium. See Article 6 of the tax treaty. Any UK tax paid will be deductible from any tax liability you have in Belgium on the same income.
As a UK national you will be entitled to the UK personal allowance as you will read here
You will need to complete UK tax returns in order to re-claim any excess tax deducted from your UK rental income. It's also the best way to record any rental losses which you will be able to deducted from rental profits in later tax years. You should have your personal allowance offset against your civil service pension via a tax coding for cash flow reasons if no other.
I'm afraid that I cannot advise you on your Belgian tax return obligations but I suspect you will need to complete them to disclose your UK income.
I hope this helps but let me know if you have any further questions.