Newcastle started striking during the reign of Stephen. These coins are rare. Rather more were produced during the Tealby coinage, but nothing during short cross, and then it reopened during long cross through to Edward I. The easiest of these is the later Edward I coinage, with everything else at least scarce.
There's nothing in the BNJ specific to Newcastle, but Allen's book on the Tealby conage refers to Askew's article in the 1941 Numismatic Chronicle pp.77-87. Sorry, don't have a copy.
During Henry II, the mint was run by William FitzErembald who also ran the mint at Carlisle. He was lessee of the mines at Alston, but eventually got into severe financial difficulties from 1170 onwards and this is the reason for the mint closure by the end of the Tealby coinage. At the end of Henry II's reign in 1189, he owed over £2150 to the crown.
During long cross there were four moneyers at Newcastle - see The Brussels Hoard book pp.164-165
Edward I coins are mentioned in the Galata guides for pennies and small change.