This source provides a complete list of the RN's vessels in service in September 1939. It lists 113 Modern Destroyers, 68 Old Destroyers, and 54 Corvette Escorts (including 4 Australian and 2 Indian), for a total of 181 destroyers and 54 Escorts. An additional 24 Modern Destroyers were under construction.
Additionally, the Royal Canadian Navy included 7 River-Class destroyers in 1939, and commissioned 1 additional River-Class and 8 Town-Class destroyers in September 1940 as pat of the WWII building program that would make it the Allies' third-largest navy, by number of vessels, in 1945. The Royal Australian Navy had the destroyers Stewart, Vampire, Vendetta, Voyageur and Waterhen in service in September 1939.
The most frequent RN organization of destroyers appears to be this:
Eight destroyers, each in the charge of a commander, plus a specially fitted leader commander (sic) by a captain, usually comprised a flotilla.
Additionally, between the wars the importance of airpower in deciding naval battles was increasingly recognized as of importance. Older destroyers without the capability of mounting A_A guns, and other modern armament, were often retired rather than moth-balled as not worth the expense of the latter. It was the surprisingly effective role of airpower in sinking the Bismarck that finally convinced the sceptics on both sides that the North Atlantic would be a battle of submarines against ASW vessels, rather than of surface fleet raiders eluding chasers.
Update comparison of Royal Navy between October 1918 and September 1939:
1918 1939 change
Battleships 34 15 -18 -54%
Cruisers 64 56 -8 -12%
Aircraft Carriers 0 7 +7 NA
B & C & AC combined 98 78 -20 -19%
Destroyers 233 181 -52 -21%
Escorts 0 54 +54 NA
D & E combined 233 235 +2 +1%
(ignoring specialty ships like minelayers, minesweepers, AA cruisers, etc.)
Contrary to the claim made in another answer, the large ships were disproportionally decommissioned in comparison to the smaller vessels.
Note also that the German submarines in World War 2 were fr the first 2 or 3 years much more effective than in World War 1, at least partially due to having broken the British and American maritime codes.
It was less about the number of destroyers available in 1939-40, as the much greater effectiveness of the Luftwaffe and Kriegsmarine in sinking them than was anticpated. In one letter to Roosevelt inquiring after the destroyers, Churchill noted that in the preceding ten days the Royal navy had had 11 destroyers sunk in the English Channel, and then precedes to list them.
The double whammy of losing the French Navy as an ally in the Mediterranean, and of the German U-boats being able to base in the Bay of Biscay and Brittany area, was completely unexpected. No pre-war planning in the Admiralty could have been expected to foresee such a rapid fall of France.