An unfortunate term, (or baited hook for tourists) most often seen when relating to;

1. A tea room/restaurant/pub situated in a historic building.
2. A tea room/restaurant/pub in the locality of a historic building, but not actually historic itself.
3. A tea room/restaurant/pub in a historic town that wants more custom than more honestly named tea rooms/restaurants/pubs. ;o)

Nowadays, the 'ye' is commonly pronounced how it looks, with a 'y' sound. However, it should correctly be prounced 'the'.

Originally, it would have been spelt using the ancient English 'thorn' character 'þ', thusly: 'þe'. The thorn character represented a 'th' sound.

However, the thorn character was not in much use in Europe outside England, and since early printing press systems came from mainland Europe, they did not have a thorn available. Since, at the time, a hand-written thorn looked much like a hand-written letter y, the y was frequently substituted.

As you can see, the modern equivalent of a typesetting system allows us to use as many thorns as we like. Alas, no-one knows how to pronounce them, any more than they know how to pronounce 'ye'.