Here in the UK we refer to county if needed to establish which town is being referred to, i.e. Newport on the Severn estuary is Newport, Monmouthshire even though it is a unitary authority now (that is, it is a county and town at the same time). Not many places that are duplicated as names are important enough for people to be aware of the others. There are many Prestons, but only one is big enough to be known nationally. The three main Newcastles all have extensions (-upon-Tyne, -under-Lyme, Emlyn) to make it clear which is referered to.
Many people still stick to the 'old' counties. I use Merseyside for my address, but a lot here use Lancashire. The Wirral fought hard to lose the L (Liverpool) post code, and now they have CH (Chester - their old county town when they were in Cheshire).
And apart from Cornwall there are some areas that regard themselves as other. The Forest of Dean doesn't seem to think it is in England or in Wales (a couple of elections ago there were 3 candidates standing for Independence for the Forest). On hearing that my father was born in Longney (on the other bank of the Severn), an old freeminer commented, 'Aye, over in England'. Then he made a remark about 'them in Wales'...