This is incorrect.
ALLIES
Royal Navy kills
1. 04 December ’39 / Salmon / North Sea / U-36
2. 25 February ’40 / Narwhal / North Sea / U-63 *
3. 16 April ’40 / Porpoise / North Sea / U-1 **
4. 20 June ’40 / Parthian / off Tobruk / Diamante
5. 20 August ’40 / Cachalot / Biscay Bay, off Nant / U-51
6. 15 December ’40 / Thunderbolt / Biscay Bay / Capitano Tarantini
7. 31 March ’41 / Roqual / S of Stromboli / Peir Capponi
8. 27 June ’41 / Triumph / Mersa Matruh / Salpa
9. 05 July ’41 / Torbay / Aegean sea / Jantina
10. 07 August ’41 / Severn / W of Gibraltar / Michele Bianci
11. 05 January ’42 / Upholder / NW of Sicily / Ammiraglio Saint-Bon
12. 30 January ’42 / Thorn / Adriatic Sea / Medusa
13. 12 February ’42 / Unbeaten / Cape Spartivento / U-374 ***
14. 18 March ’42 / Upholder / off Brindizi / Tricheco
15. 03 August ’42 / Saracen / North Sea / U-335
16. 06 December ’42 / Tigris / Cape Bon / Porfide
17. 21 January ’43 / Sahib / off Bifacio / U-301
18. 14 March ’43 / Ultimatum / Ionian Sea / Ammiraglio Millo
19. 17 March ’43 / Unbeaten / S of Calabria / Guiglemontti
20. 21 May ’43 / Sickle / S of Toulon / U-303
21. 04 June ’43 / Truculent / Norway Sea / U-308
22. 13 July ’43 / Unruly / Strait of Messina / Acciaio
23. 15 July ’43 / United / Taranto / Remo
24. 29 July ’43 / Trooper / Strait of Otranto/ Pietro Micca
25. 07 September ’43 / Shakespeare / Salerno / Velella
26. 30 October ’43 / Ultimatum / off Alger / U-431 ****
27. 09 November ‘43 / Saracen / Cape San-Vito, Sicily / Granito
28. 13 November ’43 / Taurus / off Penang / I-34
29. 15 February ’44 / Tallyho / Malacca Strait / UIT-23 (former Reginaldo Guilliane)
30. 07 April ’44 / Tuna / NW of Narwick / U-644
31. 15 June ’44 / Satyr / W of Narwick / U-987
32. 17 July ’44 / Telemachus / Malacca Strait / I-166
33. 23 September ’44 / Trenchant / Malacca Strait / U-859
34. 11 November ’44 / Venturer / Arctic / U-771
35. 09 February ’45 / Venturer / NW of Bergen / U-864
36. 12 April ’45 / Tapir / NW of Bergen / U-486
* some sources insist that U-63 was sunk by destroyer that day
** or 6 April ’40 by HMS Narwhal ?
*** or 12 January ’42 ?
**** or 21 October ’43 by Wellington bomber?
36 enemy submarines sunk, this is 25% of all warships sunk by RN submarines during the war.
18 Italian subs - 27% of all Italian submarine losses
16 German subs
2 Japanese subs
5 submarines with 2 sub-vs-sub kills each
Unbeaten, Upholder, Saracen, Venturer, Ultimatum
US Navy kills
1. 27 January ’42 / Gudgeon / SE of Midway / I-73
2. 17 May ’42 / Tautog / S of Truk / I-28
3. 17 May ’42 / Triton / S of Shikoku / I-64
4. 20 December ’42 / Seadragon / S of Rabaul / I-4
5. 15 May ’43 / Herring / Atlantic ? / U-163*
6. 27 July ’43 / Scamp / NW of Rabaul / I-168
7. 15 February ’44 / Aspro / SW. of Truk / I-43
8. 23 March ‘44 / Tunny / S. of Palau / I-42
9. 28 April ‘44 / Pogy / E of Kyushu / I-183
10. 26 June ‘44 / Sawfish / South China Sea / I-29
11. 15 September ‘44 / SeaDevil / E of Honshu / I-364
12. 09 November ’44 / Flounder / Java Sea / U-537
13. 29 November ‘44 / Scabbardfish / SE of Tokyo Bay / I-365
14. 10 June ‘45 / Skate / Sea of Japan / I-122
15. 15 July ‘45 / Bluefish / Off Borneo / I-351
16. 14 August ‘45 / Spikefish / China Sea / I-373
17. 09 February ‘45 / Batfish / NW of Luzon / Ro-115
18. 10 February ‘45 / Batfish / NW of Luzon / Ro-113
19. 12 February ‘45 / Batfish / NW of Luzon / Ro-112
20. 24 February ‘45 / Lagarto / E of Kyushu / I-371
21. 23 April ’45 / Besugo / Java Sea / U-183
* according British sources U-163 was sunk by Canadian corvette “Prescott” 13 march ’43 in North Atlantic.
18 Japanese submarines (15 % of all Japanese submarines losses)
3 German u-boots
Submarine with 3 (!) sub-vs-sub kills – Batfish
Soviet Navy kills
1. 09 August ’41 / Sh-307 / Finnish bay / U-144
2. 28 August ’43 / S-101 / Karsk sea / U-639
3. 14 December ’44 / Lembit / Finnish bay / U-479
Dutch Navy kills
1. 28 November ’41 / O-21 / off Almeria / U-95
2. 09 February ’43 / Dolfin / S of Sardinia / Malacite (Italy)
3. 06 October ’44 /Zvaardfisch / Java Sea / U-168
Norway Navy kills
1. 19 April ’44 / Ula / North Sea / U-974
64 Axis submarines were sunk by Allied subs.
AXIS
U-Boots kills
1. 10 April ’40 / U-4 / AN2989 Skudenes fiord / HMS Thistle
2. 09 May ’40 / U-9 / AN8511 / Doris (French)
3. 01 August ’40 /U-34 / AN4281, Cape North Head / HMS Spearfish
4. 19 December ’40 / U-37 / DH96 Cape Hubi / Sfax (French)
5. 23 June ’41 / U-144 / AO6486, off Vindava / M-78 (Soviet)
6. 26 June ’41 / U-149 / AO2982 / M-101 (Soviet)
7. 21 July ’41 / U-140 / AO6139 / M-94 (Soviet)
8. 10 January ’42 / U-584 / AC8493 / M-175 (Soviet)
9. 18 April ’43 / U-123 / 0649N-1309W / P-615 (British)
10. 15 November ’43 / U-565 / CO36, NW of Rhodos / HMS Simoom *
* underwater encounter, British sub was sunk by T-V acoustic torpedo, no hard data though.
Italian Navy Kills
1. 06 October ’40 / Tricheco / 33.30N-27.18E / Gemma (Italy) *
2. 15 October ’40 / Toti / 33.16N-17.37E / HMS Rainbow
3. 16 July ’41 / Nereide / 37.25N-25.52E / Triton (Greece)
4. 18 June ’42 / CB-3 / CL5546 / Sh-208 (Soviet)
5. 26 August ’43 / CB-4 / CL5164, Cape Tarhankut / Sh-207 (Soviet)
* by mistake
IJN Kills
1. 25 December ’41 / I-166 / off Kuching / K-XVI (Holland)
2. 11 October ’42 / I-25 / 46.41N-138.56W / L-16 (Soviet) *
3. 16 November ’43 / I-176 / S of Truk / USS Corvina
* by mistake
Finnish Navy
1. 21 October ’42 / Vesihiisi / AO2826 / S-7 (Soviet)
2. 27 October ’42 / Iku-Turso / AO23??, Oland sea / Sh-304 (Soviet)
3. 05 November ’42 / Vetehinen / AO23?? Oland sea / Sh-305 (Soviet)
20 Allied and 1 Axis submarines were sunk by Axis subs.
This list is fairly accurate to my knowledge and a simple demonstration of the number of times such a thing occured in WW2. Submarine versus Submarine action also occured in WW1.
Finally
The Royal Navy would disagree with you, they hold the perisher course for SSN's (no longer for SSK's I believe Denmark or Norway hold it now?). One of the biggest duties of a Royal Navy submarine is defence of the fleet from other submarines.
The US also practices this.
Where did you formulate this opinion of yours?