Please refer to section 5 of HMRC6 as part of my answer to your questions.
As you are not domiciled in the UK you have several choices as to how to deal with non-UK source income and gains as follows:
1 Overseas income or gains you bring into the UK may be taxable in the UK (see below on money held before you came to the UK). Depending where it comes from and assuming there is a double tax treaty between the UK and the country of origin, you will be able to offset any foreign tax paid on that income or gains against your UK tax liability if you have one on the same income.
2 Paragraph 5.1.1 of HMRC6 deals with very small amounts of non-UK income. If you meet the criteria set out there and have less than £100 of overseas bank interest, you won't have to pay UK tax on it.
3 If you have overseas income which you have not brought into the UK of under £2,000 in any one tax year you can use the remittance basis of assessment which means that you do not have to pay tax on that unremitted income. You will keep your entitlement to the UK personal allowances and Capital Gains Tax exemption. See paragraph 5.5.1 of HMRC6.
4 If the unremitted income is £2,000 or more and you don't want to pay UK tax on it, you will need to make a claim for the remittance basis of assessment to apply. You may lose your entitlement to the UK personal allowances and the Capital Gains Tax exemption. See paragraphs 5.5.2 and 5.6 of HMRC6. In addition, depending on how long you have been in the UK, you may have to pay the Remittance Basis Charge of £30,000 or £50,000 for any tax year you choose to be taxed on the remittance basis . See paragraph 5.7 of HMRC6 and section 1 of the document here for more information on the RBC.
In order to avoid paying UK tax on foreign source income and gains that you earned or made before you came to live in the UK, you really need to separate that money from foreign source income and gains you have made since your arrival in the UK. Then , if you need to being money from abroad into the UK, you can draw on funds you had before your move to the UK and be able to demonstrate the fact if you are asked by HM Revenue & Customs.
If your father gifts you some money, you would not have to pay UK tax on that money. There may, however, be Inheritance Tax issues for your father's estate if he dies within seven years of making the gift and it is made from assets held in the UK, though not from foreign currency accounts held in UK banks.
I hope this helps. Let me know if you have any further questions.