Jim Clark won the British Grand Prix 1964 at Brands Hatch on 11 July 1964, starting from pole position. Graham Hill finished second for BRM, with John Surtees completing the podium for Ferrari.
| Pos | Grid | Driver | Team | Laps | Time / Status | Pts | FL |
|---|---|---|---|---|---|---|---|
| 1 | 1 | Jim ClarkCLA | Lotus-Climax | 80 | 2:15:07.0 | 9 | |
| 2 | 2 | Graham HillHIL | BRM | 80 | +2.8 | 6 | |
| 3 | 5 | John SurteesSUR | Ferrari | 80 | +1:20.6 | 4 | |
| 4 | 4 | Jack BrabhamBRA | Brabham-Climax | 79 | +1 Lap | 3 | |
| 5 | 8 | Lorenzo BandiniBAN | Ferrari | 78 | +2 Laps | 2 | |
| 6 | 15 | Phil HillHIL | Cooper-Climax | 78 | +2 Laps | 1 | |
| 7 | 7 | Bob AndersonAND | Brabham-Climax | 78 | +2 Laps | 0 | |
| 8 | 14 | Richie GintherGIN | BRM | 77 | +3 Laps | 0 | |
| 9 | 13 | Mike SpenceSPE | Lotus-Climax | 77 | +3 Laps | 0 | |
| 10 | 10 | Innes IrelandIRE | BRP | 77 | +3 Laps | 0 | |
| 11 | 16 | Jo SiffertSIF | Brabham-BRM | 76 | +4 Laps | 0 | |
| 12 | 21 | Giancarlo BaghettiBAG | BRM | 76 | +4 Laps | 0 | |
| 13 | 3 | Dan GurneyGUR | Brabham-Climax | 75 | +5 Laps | 0 | |
| 14 | 20 | John TaylorTAY | Cooper-Climax | 56 | +24 Laps | 0 | |
| R | 9 | Jo BonnierBON | Brabham-BRM | 45 | Brakes | 0 | |
| R | 22 | Peter RevsonREV | Lotus-BRM | 43 | Differential | 0 | |
| R | 17 | Tony MaggsMAG | BRM | 38 | Gearbox | 0 | |
| R | 23 | Ian RabyRAB | Brabham-BRM | 37 | Accident | 0 | |
| R | 18 | Trevor TaylorTAY | Lotus-BRM | 23 | Driver unwell | 0 | |
| R | 12 | Mike HailwoodHAI | Lotus-BRM | 17 | Oil pipe | 0 | |
| R | 11 | Chris AmonAMO | Lotus-BRM | 9 | Clutch | 0 | |
| R | 6 | Bruce McLarenMCL | Cooper-Climax | 7 | Gearbox | 0 | |
| R | 19 | Frank GardnerGAR | Brabham-Ford | 0 | Accident | 0 | |
| F | 25 | Maurice TrintignantTRI | BRM | 0 | Did not qualify | 0 | |
| W | 24 | Richard AttwoodATT | BRM | 0 | Withdrew | 0 |