If you are a UK resident and UK domiciled individual, you would be chargeable to UK income tax on your worldwide income, this would include overseas rental income (subject to the terms of any relevant double tax treaty).

A common scenario is for a UK resident to own an offshore property via an offshore company. You would then need to consider whether the company is UK resident.  

A company is resident in the UK if it is either a UK incorporated company, or if its central management and control is located in the UK.

If a UK resident company, it would be subject to UK corporation tax on its worldwide income.

You are allowed to deduct all expenses incurred in letting the property as management expenses.  Therefore any repairs, agency fees etc will be deducted from the rental income.

The interest on a mortgage, where the funds were used to purchase the let property would ordinarily be allowed as a tax deduction. However, if the mortgage is incurred by you personally, you would need to effectively recharge the company for the interest paid to qualify for a tax deduction in the company. This could then allow the extraction of cash free from the company.

If the company could be argued to be non UK resident, there would be no corporation tax charge on its income, however, you would be liable to UK income tax on income received from the company (assuming you are both UK resident and domiciled). There would also be anti avoidance provisions to contend with that could in any event attribute the income of the non resident company to you and your partner.