I am a dual national and I hold a British passport; can I apply for a visa?

No. If your passport - or expired passport - identifies you as a British Citizen (GBR), you do not need to apply for a visa.
British Citizens (GBR) including those who are dual nationals, are not required to have a visa for the UK. A visa will normally impose certain conditions on someone's entry (including 'no work'). The immigration rules do not apply to British Citizens (including holders of expired British citizen passports) visa officers will therefore not be able to issue a visa to a British Citizen. If you decide to submit an application for a visa, and you have paid a fee and your biometrics have been submitted, no refund will be given.
If you hold a British national passport (that is, British Overseas Territories citizen; British Overseas citizens; British National (Overseas); British Protected Persons; British Subject), you will need to check whether you need entry clearance.