Hi Mark,
Going by Google map streetview of St Alban's the gravestone style look much older than 1834- so took it for granted it was the Heworth chapelry. Though its say St Mary's was founded 1822 and get more complicated:
https://www.genuki.org.uk/big/eng/DUR/HeworthExtract from link
" "Heworth Church, St. Mary's, was probably founded by Ceolfrid, abbot of Monkwearmouth and Jarrow, within two years of the consecration of Jarrow Church, A.D. 684. The twenty-three coins of the realm of King Ecgfrid,
found in this churchyard in the year 1812, prove this, as they were most likely dedication coins placed under the foundation-stone of the original church; and as King Ecgfrid was killed in 685, this was probably the year in which the foundation-stone was laid. From that time until 1214 no further mention is made of this church, but in a record of that year reference is made to
"the lands of the chapel of Heworth," and since that time notices of it are frequent. It was rebuilt in 1684, and again in 1711, at which date it was considerably enlarged. The present edifice was erected on the same site in 1822, and is a fine cruciform structure of stone in the Early Decorated style, with nave, transepts, shallow chancel, and square tower at the west containing a clock. The living is a vicarage, valued at £280, in the gift of Lord Northbourne, and held by the Rev. James Steele."
[From History, Topography and Directory of Durham, Whellan, London, 1894]