While the repair capacity might have existed the RN began to take a more pragmatic view from mid-war. So in 1939/40 significantly damaged ships were repaired, sometimes at great cost in time and resources. The following come to mind:
Belfast - mined. Repairs took nearly 3 years.
Eskimo - destroyer. Lost bow at Narvik. Rebuilt
https://en.wikipedia.org/wiki/HMS_Eskimo_(F75)#/media/File:HMSEskimoBowTorpedoDamageMay1940.jpg
Javelin - destroyer. Lost bow and stern (Over half her length). Rebuilt.
From 1943 there are some of ships not repaired despite mine, bomb or torpedo damage. These immediately come to mind.
Porcupine - destroyer torpedoed Dec 1942. Cut in two and towed home for scrap
Derwent - Hunt class victim of aerial torpedo March 1943. Not repaired.
Chanticleer - sloop victim of a T5 in Nov 1943. Not repaired. Became a base ship in Azores.
Carlisle - cruiser bombed in Aegean Oct 1943. Not repaired. Became base ship at Alexandria.
RHNS Adrias - Hunt class destroyer mined in Adriatic Oct 1943 losing bow back to bridge. Not repaired. Compare to Eskimo above.
View attachment 824645
Loyal - destroyer mined Adriatic Oct 1944. Not repaired.
Pathfinder - bombed Burma Feb 1945. Not repaired.
Escort carriers Nabob (Aug 1944) and Thane (Jan1945) torpedoed but not repaired.
8 Captain class frigates in 1944/45 - badly damaged from various causes but not repaired.
5 RN/RCN River class frigates mostly victims of T5s. Not repaired.
Salamander - minewweeper victim of friendly fire Aug 1944. Not repaired.
Wensleydale - Hunt class Dec 1944 damaged in collision with LST. Not repaired.
Goathland - Hunt class mined July 1944. Not repaired.
Fury - destroyer mined and suffered collision damage June 1944. Not repaired.
With plenty of new ships entering service, from mid-1944 the repair effort in British yards was going into work relating to ships and vessels destined for campaigns in the far East. "Non standard" US built vessels were just an added complication.