I have been in the USA for a a few years during when I lost my Brtitish passport.. I just got it replaced by the British embassy because I have to travel to UK urgently. As I do not know how long I am going to be in the UK, I intend travelling on a one-way ticket.
Do I need a visa to get out of the USA? As a British citizen, do I just pick my passport and travel? Pls advise.
That's exactly what u need to do. Just get the passport and go. U get visa on arrival.
You wouldn't normally need a visa to leave a country - typically a visa is required for entry and to stay.
To get into the UK you only need a visa if you do not have a british passport/EU passport or docs.
However you should check what your status would be to get back into the US should you feel that is an option in future and should you be on a visa for the US - they can have some tricky rules about return entry. The UK embassy would be the best place to contact.