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Let me take at this and I'll get back to you in a bit.
Even if you are non-UK resident, you may still pay UK tax on your rental income profit but you should be entitled to the UK personal allowance of £11,000 (see boxes 15 and 16 notes here) which will cover your rental income, even before expenses are deducted such as mortgage interest so you should pay no tax in the UK. Take a look here for the types of expenses you can claim. So long as you are not married, you and your partner can split the rental income in any way you like for tax purposes. Child benefit isn't taxable. There are some useful notes for non-UK resident landlords here.
As a non-resident landlord, you will need to register with HMRC who will put you into the self-assessment system. Your letting agent will be obliged to deduct tax from your rental income which you can reclaim if you have no liability. You can apply to have your rental income paid without deduction of tax if you meet the criteria set out in form NRL1. Having no tax liability is one of them. Your UK tax affairs must be up to date. Even if you have no UK tax liability, HMRC may ask you to complete a tax return so you should keep records of your rental income and expenses.
I hope this helps but let me know if you have any further questions.
Complete and submit to HMRC the NRL1. They will put you into the self-assessment system as a non-resident landlord. You may be issued with a tax return to complete, probably for 2016/17 which ends on 5 April 2017. Keep good records of your rental income and expenses. Answer any questions HMRC may have. Complete your tax return on time. There really isn't much to it. You could get a UK accountant or tax adviser to do it for you.
I'm just following up to find out if my answer helped or if you have any further questions.
Thanks and good luck.