Thank you so much everyone for all your help. That Routledge Terrace was renamed Hollycarr Terrace certainly seems to be the answer to my question. And when I checked on the house numbers, I found that my grandfather was living at 16 Routledge Terrace in 1891, then at 16 Hollycarr Terrace in 1901, so hadn't moved house as I'd imagined.
Spelk mentioned Vinegar Hill. "What’s in a name: Street names of Sunderland" says that Harvey Terrace, Hollycarr Terrace, Hugh Terrace, Leechmere Terrace, Powell Terrace, Sidney Terrace, South View, Streatfield Terrace, Sunderland Terrace and West Terrace were all miners' cottages, no longer in being, that were in an area of Ryhope known as Vinegar Hill. 'They rank as an important part of the village's mining history, however.'
Once again, many thanks to you all.