The Hale Rocket was an improvement on the earlier Congreve rocket, but still not really that good as a weapon of war. The imperial authorities considered best as a way of scaring unsophisticated natives, and sailors from HMS Active used them against the Zulu Kingdom, who were anything but unsophisticated when it came to war, with limited success.
The rocket was developed by William Hale and patented by him in 1844. His key innovation was to have the exhaust gasses escape from the rocket through angled nozzles. This caused the rocket to spin like a bullet from a rifle and gave it much greater accuracy than previous types of rocket. During the Zulu War one rocket team managed to hit the same building with three rockets; however this was exceptional. Most of the time they were still wildly inaccurate, and could even turn around and end up coming strait back at the men that had fired them. By making the rocket spin to stabilise it also allowed Hale to get rid of the long tail that had been a feature of all previous rockets. This reduced rockets drag and allowed it to go further.
Both of the services used Hale Rockets, but they used different launching technologies. The army fired their rockets along an open trough, while the navy fired them through a tube. They could be up to 60 pounds, but the ones used by the British were 9lb or 24lb with ranges of about 1 mile and 1.5 miles, respectively. The rocket had gunpowder warhead that was triggered by a fuse that ran down the body of the rocket, but given their woeful accuracy they were mainly a weapon designed to terrify opponents, or for mass bombardment.
With the creation of breech loading rifled guns rockets rapidly fell out of favour. Breech loading meant that guns could be loaded and fired just as fast of rockets, and rifling meant that they became more accurate than them. There was a small use of rocket weapons against balloons and Zeppelins during WW1 since their fiery exhaust could ignite hydrogen gas bags were solid artillery shells would just punch holes in them. Rockets were also used by the RNLI and Coastguard for firing lifelines to ships that had run aground but it was not until the second world war when rockets would again become a significant weapon system.