Actually, in 1801 the British did not sink and capture the Danish fleet - and only half of the fleet was committed to the battle - whereas in 1807 - at a time when Denmark was neutral, Britain invaded, laid siege to Copenhagen, and in the aftermath sailed off with the fleet (so, not a consequence of a naval battle). This heinous act drove Denmark into an alliance with Napoleon, and, in the end, cost us Norway, as Denmark did not, like for instance Bernadotte in Sweden, act as a turncoat in 1813 (for which he got Norway).
My point is, had Nelson faced a fully prepared Danish fleet (which was, as I recall it, almost as big as the British) in 1801, there might not have been a Trafalgar 4 years later.