Before (end of 1978) (35 seats, Elections Centre)
Other 35 · The Liberal Party 0 · Conservative 0 · Labour 0
After (end of 1979) (34 seats, Elections Centre)
Other 34 · The Liberal Party 0 · Conservative 0 · Labour 0
Ward results
Askrigg1 seat · turnout 75.1%
| J. Abraham | Independent | 306 |
| S. Metcalfe | Independent | 248 |
Bolton Manor1 seat
| C. Waite | Independent | 0 ✓ |
Catterick & Tunstall2 seats · turnout 61.3%
| H. Proom | Independent | 751 |
| S. Proom | Independent | 588 |
| G. Pullan | Independent | 455 |
| J. Gudgin | Independent | 371 |
Colburn3 seats · turnout 42.8%
| G. Nickling | Independent | 921 |
| H. Mudd | Independent | 539 |
| L. Jeff | Independent | 529 |
| P. Stock | Independent | 507 |
| J. Church | Independent | 340 |
Croft-On-Tees1 seat
| R. Pease | Independent | 0 ✓ |
| W. Alderson | Independent | 0 ✓ |
Hawes and High Abbotside1 seat
| W. Metcalfe | Independent | 0 ✓ |
Kirby Hill1 seat
| C. Watson | Independent | 0 ✓ |
Leyburn2 seats
| B. Cowell | Independent | 0 ✓ |
| Karl Jones | Independent | 0 ✓ |
Lower Dale1 seat
| J. Potts | Independent | 0 ✓ |
Lower Swaledale1 seat · turnout 60.8%
| K. Bayley | Independent | 128 |
| M. Smalley | Independent | 65 |
| E. Williams | Independent | 64 |
Middleham & Coverdale1 seat
| E. Collins | Independent | 0 ✓ |
Richmond Central1 seat
| R. Cross | Independent | 0 ✓ |
Richmond East3 seats · turnout 49.2%
| D. Waldie | Independent | 1,083 |
| K. Carr | Independent | 1,030 |
| A. Harris | Independent | 987 |
| S. Oliver | Independent | 729 |
Richmond West2 seats
| R. May | Independent | 0 ✓ |
| B. Thompson | Independent | 0 ✓ |
Scotton1 seat
| M. Rothwell | Independent | 0 ✓ |
St. Agathas1 seat
| K. Spurgeon | Independent | 0 ✓ |
St. Michaels & St. Lukes1 seat
| W. Corps | Independent | 0 ✓ |
Swaleside1 seat · turnout 77.0%
| R. Leggett | Independent | 312 |
| M. McGill | Independent | 189 |
| J. Hendren | Independent | 133 |
Urevale1 seat · turnout 71.8%
| J. Woodrow | Independent | 317 |
| G. Hodgson | Independent | 233 |