What are my chances of being granted an emergency travel document to the UK?

You can in theory apply for an Emergency Travel Document if you are outside Britain and have lost your passport and need to travel. However the normal purpose is to allow you to return to the UK when you have no other travel document. It is uncertain if wishing to go to a relative's funeral constitutes an emergency. It may depend on how close a relative it is.

You should be aware that if you have lost your British passport you are obliged to report it when you realize you have lost it. A lost passport may be used illegally if someone else finds it.

Proof of being born in the UK is not proof of British citizenship, so your Ghanaian passport will not get you into Britain, even if it were valid.

Could travel with my expired Ghanaian passport?

You cannot travel out of Ghana on an expired passport. I am a Ghanaian and I know this because I checked something similar including traveling to Ghana on a US passport with my expired Ghana passport as proof of citizenship.

Not only will the immigration at Kotoka Airport not allow you, but the airlines at Kotoka will not even allow you to check in before getting to the immigration gate. If they do, the immigration will stop you, fine you, and request you get a new passport or travel document

Before I book a ticket, what is the likelihood of me being granted a emergency travel document?

I will defer this part of the question to the UK immigration experts here.