Hi.Even if you are non-UK resident, you may have to pay tax in the UK on any surplus of rental income over deductible expenses such as mortgage interest, repairs etc. Take a look here for a more comprehensive list of deductible expenses. You would also be subject to the rules of the non-resident landlord scheme which you can read about here. Assuming you are a UK national, you will be entitled to a personal allowance to offset against your rental income and other taxable UK source income.Take a look here for information on the tax situation of a non-UK resident non executive director, in particular the last two paragraphs. There is some more useful guidance here. Fees for work carried out in the UK will be taxable in the UK. Where there is a mix of UK and non-UK duties, HMRC will need to be approached to agree a formula which can be applied to your situation to determine any fees not taxable in the UK.
I hope this helps but let me know if you have any further questions.