@JimWarI live in Washington State, in the USA, but I used to travel to Canada frequently. Among the reasons was to purchase a British monthly magazine: Wargames Illustrated.
Over the years they had at least 2 interesting articles about Smuggling during the French Revolution and Napoleonic Wars.
They briefly talked about the history prior to the French Revolution (to avoid tariffs, port fees, and taxes). With the revolution Frech luxury goods, such as Brandy, other liquors, and such became both more lucrative, and smuggling increasingly dangerous. British authorities were concerned about spies or saboteurs being landed. The situation in France reduced the supply, and war increased the "need" for taxes, resulting in even more incentives to smuggle.
In the early 1800's Emperor Napoleon I attempted to impose the "Continental System" to deny trade and goods to the UK; the British Royal Navy blockade of the Continent also resulted in further incentives to smuggling.
Smuggling into the UK (and perhaps even some out) occurred nearly everywhere. However, patrols (naval and ashore) were heavier nearer the major Ports and beaches nearest to Normandy and the Pas de Calis.
Cornwall, and to a lesser degree Sommerset were notorious for smuggling So, to the Fens of east Kent, as well as the Tees and Tynemouth, Wales, Scotland, and Ireland all had areas where smuggling occurred.
Wargames Illustrated included "Skirmish Scenarios" based upon historic records. Smuggling was concerning enough to the British Government that detachments of Cavalry or Yeomanry (in that era they weren't Longbowmen, but Militia Cavalry, typically the sons and cousins of the Gentry); Light Dragoons were preferred. However, other types of Cavalry/Yeomanry, or even Infantry or Militia may be used to augment British Customs personnel.
(I believe the County Sheriffs, and in some locations "Borderers" or other military or para-military forces might be used.)
Typical Patrols were probably 4 to a dozen. 2-4 Customs (or possibly other law enforcement personnel; remember there were no Police or "Bobbies" at this time, or for a few decades more) Shire Reeves/Sheriffs were responsible for Tax Collection/enforcement; so, they might be persuaded to contribute some constables or other men to enforce customs (taxes) {Customs enforcement was NOT the typical jurisdiction of Sheriffs} Bounties (and/or confiscation) could be an incentive for a Sheriff, or Colonel in Chief of a Militia (infantry) or Yeomanry (Cavalry) Regiment to "volunteer" a few men. Regulars of the Royal Army would be ordered by "Horse Guards" (the location of the British Royal Army).
This would NOT be an entire Regiment. Rather, several individuals, to several dozen would volunteer/be "volunteered" if it was a larger number they would be spread out in penny packets along a considerable stretch of coast line (including up rivers).
From what I read a "typical" patrol would be 4 to 6, in rare circumstances up to a dozen. A couple Customs Officials (in the late 1700's I believe that a "senior" customs official paid a "license" {or perhaps an outright bribe} for the Office; they would then hire some "Toughs" (and "Sneaks") and receive a percentage of confiscated goods (or money/silver or other valuables) {perhaps not all "confiscated" goods were reported; coins (etc.) in particular might end up in peoples' pockets.
If there were a tip (or other "Actionable Intelligence" not a term of art at the time), then perhaps a dozen, or even a score (20) of Customs agents and soldiers might be concentrated (doing so would leave a considerable are un patrolled, so not common).
Unfortunately, many of my resource materials have been packed away for my pending move.