How did British divisions reform after Dunkirk? Were they disbanded to make new ones, or was an effort made to reunite the scattered personnel from across the country? How did the British "put their army back together"?

The following British division-sized formations participated in the battle for France in summer 1940

Unit	Fate during Dunkirk Evacuation	Post-Dunkirk Activities
1st Infantry Division	Successfully evacuated	Served in North Africa, Italy, and the Middle East
2nd Infantry Division	Successfully evacuated	Served in India and Burma
3rd Infantry Division	Successfully evacuated	Served in Northwest Europe
4th Infantry Division	Successfully evacuated; suffered heavy losses	Reconstituted and served in North Africa, Italy, and Greece
5th Infantry Division	Successfully evacuated	Served in India, the Middle East, Sicily, Italy, and Northwest Europe
23rd (Northumbrian) Infantry Division	Successfully evacuated; suffered very heavy losses	Disbanded in June 1940 with remains going to the 50th (Northumbrian) Infantry Division and other units
42nd (East Lancashire) Infantry Division	Successfully evacuated; suffered heavy losses	Disbanded and converted to the 42nd Armoured Division; disbanded again in 1943
44th (Home Counties) Infantry Division	Successfully evacuated; suffered heavy losses	Reconstituted and fought in North Africa; disbanded in 1943
48th (South Midland) Infantry Division	Successfully evacuated; suffered heavy losses	Served in England for the remainder of the war
50th (Northumbrian) Motor Infantry Division	Successfully evacuated; suffered heavy losses	Reconstituted and served in North Africa, Sicily, and Northwest Europe
51st (Highland) Infantry Division	Served as part of rearguard; destroyed with most men taken prisoner	Reformed in England by re-designating its Territorial Army copy, the 9th (Highland) Infantry Division, in August 1940; served in North Africa, Sicily, and Northwest Europe
52nd (Lowland) Infantry Division	Successfully evacuated	Served in Northwest Europe

The division-sized units that were successfully evacuated from the beaches of Dunkirk received time to rest and reform using draftees and volunteers collected from across the British isles, and then were posted to coastal defense duties in anticipation of the expected German cross-channel invasion. Due to their experience in World War I and the limited manpower available to them, the British were very leery of blindly committing large numbers of infantry to battle, and so husbanded their available men carefully, or until it was no longer possible to do so. Many of the involved units had lost most or all of their heavy vehicles (including tanks), artillery pieces, and equipment, and were effectively neutered until these supplies could be restored. Fortunately, Operation Sea Lion never occurred, and many of the still-active involved units began to deploy overseas to the various theaters of war the British Empire was involved in. Only three of the divisions involved at Dunkirk never saw combat again in their original or a related form, the 23rd (Northumbrian), 42nd (East Lancashire), and 48th (South Midland) Infantry Divisions.