Wells notes that rhyming fur and bear (also known as the “fur-bear merger”) is “a well-known characteristic of Scouse, the broad accent of Liverpool and Merseyside”; he also states that it extends to parts of Greater Manchester and Lancashire (1982: 361).
Upon first inspection it appears as though fur and bear aren’t really rhymed anywhere in great numbers. However, there is a very concentrated cluster of speakers just to the west of Manchester where the merger is prominent. This covers much of Merseyside, and extends to St. Helens, Wigan, and parts of Bolton and Preston in Lancashire. It is also present in the speech of a fair number of speakers from Northern Ireland.