You need an ETA for United Kingdom if you have a Taiwanese passport

Travelers visiting the UK for under six months require an Elecronic Travel Authorization (ETA). Travelers can submit an ETA application online. Once the application is approved, travelers receive their ETA confirmation electronically. An eTA is electronically linked to a passport and valid for up to 2 years. If travelers receive a new passport, they must apply for a new eTA. Travelers visiting the UK for more than six months, for example to live, work or study in the UK, should check the source for more details. For travelers who are existing visa holders who live in the UK and use a physical immigration document to prove their rights, the UK is moving from physical immigration documents to eVisas. Travelers with existing visas should take action now to create a UK Visas and Immigration account to access their eVisa. The ETA requirement doesn’t apply to: - Travelers who are dual citizens with British or Irish citizenship. Dual citizens must prove their permission to travel using a British passport, Irish passport, or other passport containing certificate of entitlement to prove they have right of abode in the UK; - Travelers with a valid visa; - Travelers with permission to live, work, or study in the United Kingdom (including settled or pre-settled status or right of abode); - Travelers who live in Ireland traveling from Ireland, Guernsey, Jersey, or the Isle of Man; - Travelers transiting through the United Kingdom via Manchester Airport (MAN) or Heathrow Airport (LHR) who will not pass through border control (‘airside’ transit). Visit the source for more details.