I'm a little earlier in the era of Napoleonic Wars but I might be able to provide some answers to your question. I want to take a guess that this question might be inspired by Richard Sharpe and his adventures in the British army. There will be a bit of explanation on how the system worked so as it really understand why few merit promotions existed. For the uninitiated, before the late 19th century the British army had officers pay for their ranks in the form of commissions. Men would have to literally purchase their next rank if they wanted to be promotion. This ended in 1871 as part of the Cardwell Reforms. Enlisted and Non-Commission Officer ranks did not require this, only Commissioned Officer ranks did.

The commissions started in the late 17th century after the end of Cromwell's army. For two reasons: To create a barrier for those not worthy of entry and to force investment of men that wanted to be of the commissioned officer class. The prices were quite hefty and most people of anything less than middling would not be able to afford the lowest rank of Ensign or Cornet if Horse regiment. This was the price for just the rank and nothing else. The officer had to provide his own equipment and often uniform, which created more expenses and possibility of debt. The force of investment meant that the army wanted those who could sustain themselves on their own income and little with the army's. The army learned their lesson during Cromwell's time since a lot of the army officers and leaders would have all expenditures covered by the army's treasury and none of their own. The lavish lifestyle they put on themselves pulled the army into debt, especially after the war ended. By changing that perimeter officers would be paid a standardized rate on a yearly basis.

The commission ranks went from ensign/cornet to colonel. Higher ranks such as general did not have to capability to be purchased. A colonel or such could be promoted to general but was not a purchased rank. The rank of brigadier general was a temporary one during wartime. I would also like to distinguish the British army confusingly often had two ranks for officers. An officer could have a rank in his commissioned regiment and different one in the army simultaneously. Positions such as the brigadier general, aide de camp, and brigade majors were positions in the army, which were not the same as in the regiment. For example: Lord Cornwallis was the colonel for the 33rd regiment of foot but had the rank of general (at first major then lieutenant general) in the army. It gets more complex with the Guard regiments so I will leave it at this for now. The ranks above colonel were appointed by higher ranked military leaders.

How many went from enlisted to commissioned officer ranks, and then to the really high ones? Very few. While it was possible for a sergeant to gain a promotion to ensign from a battlefield commission, it was rare, and any other promotion would have to be bought by the ensign. So while his initial promotion would be bought and paid for, the next one he would have to cover - a huge expense for an officer with no other means. One would sell the current commission to make up the different for the next rank, but for a person that came from the ranks the extra hundred pounds was not easily to acquire. The rise through the ranks is more common to the British Royal Navy than to the army. One example I can provide is James Inglis Hamilton. A third son of a family, he enlisted in the British army in 1755, which means he joined as the lowest rank, and eventually obtained the rank of brigadier general in the America War of Independence. Very few others have had the same privilege and experience as Hamilton did. Some sergeants got promotions to ensign and did not reach any higher. The sergeants promotion could have come from a battlefield promotion from an action in battle that the commander deemed worthy.

Going from one officer position to another also depended on availability. One way to gain entry to officer ranks was joining a regiment as a gentleman volunteer. The man would have a minimal income and share some social status with officers but did not hold rank. They waited for an opening to occur, such as the promotion of an ensign or his death. The opening did not always go to the volunteer, other prospect ensigns may have had the better opportunity such as an actual purchase of the commission from the previous ensign. John Peebles of the Royal Highland regiment in the American War of Independence began his career in the French and Indian war as a surgeon's mate, but by 1775 he was a lieutenant. His relationship with the commanding officers put him in the eyes for promotion but it only came when vacancy appeared. He soon had a promotion to captain-lieutenancy, the rank of captain but the pay of lieutenant (rather a bad bargain of a rank I might add) and only until later did he receive full promotion to captain of the grenadier company. His career would end at captain since the service of the 42nd in the war stalled to a halt. He realized he would not be able to gain the rank of major at any rate. He had the funds but lacked the opportunity. Even if a majority opened up in another regiment, other captains in that regiment had first stab at it. So with the current majority in the 42nd occupied and not moving, he had no other rank to move to. Peebles also had no chance of gaining a rank in the army either since all the positions filled by then. Staff officership stayed quite stable throughout the war.