First, it is crucial to understand Britain's strategy before the fall of France. Natural geography would allow the U-Boat threat to be somewhat contained in the North sea through sealing the straights of Dover and active patrolling and mining of the north sea in a line from the Orkneys and Shetlands to Norway. This would additionally blockade German ports, protect British shipping lanes, and allow for the build-up of empire and dominion forces in Britain prior to their deployment in France. The RAF would be primarily fighter orientated to protect British cities, through with a increased portion of bombers and coastal patrol aircraft to attack German industry and aid the Royal Navy’s efforts.

These measures would allow for a significant portion of Britain's manpower to be deployed into the army. During the 20s and 30s, fierce spending cuts had caused severe economies in army funding, however this was balanced by domestic, political and military desires to create a material orientated army to avoid the bloodshed of the western front. Its weaponry- cruiser tanks, Bren guns, Bren carriers, 2 inch mortars and 25 pounder guns, prized mobility over firepower, while economising on manpower. The proposed large inter-war army (of some 60-70 divisions) would mirror this, but would demand significant combat and service support, and would take significant time to be armed, trained and deployed, reflecting the British appreciation that military effectiveness lay in proficiency across the board of military activities, rather than their opponent’s narrow emphasis upon combat and maneuvre. The BEF of territorials and regulars, in combination with their French allies would hold out until this massive force was properly prepared for combat. This army would consequently arrive once French and German manpower reserves had been exhausted, allowing them to secure victory and a position in the world where Britain could exercise considerable post-war influence.

The fall of France however changed all of this. Instead of the French army bearing the brunt of the 400 division strong German army, Britain would have to face this behemoth alone. German U-boats, operating from Atlantic and Mediterranean ports would be able to attack British shipping over far greater areas of water, while British Cities would face the undivided attention of the Luftwaffe.

Consequently the RAF, the Royal Navy and the Merchant Marine received the lion's share of Britain's manpower reserves, as they represented the best means of ensuring Britain's continued survival, while striking at the Germans. The Navy and Merchant marine demanded considerable resources so as to hunt the U-Boat threat and maintain its numbers in the face of considerable losses. The RAF would defend British cities while a massively expanded bomber command represented a means to strike at their enemy.

The battered British army, withdrawn from Dunkirk, was to become the nucleus of a much smaller force- 35 divisions total. This was partially offset by a production run of equipment and weaponry sufficient to arming a total of 55 divisions, providing material for resistant groups and the arming in Britain of free French, Norwegian, Dutch Belgian and other formations. The resistance groups, in combination with rapid amphibious and airborne assaults and a variety of unconventional forces (commandos, paras, SAS, SOE operatives) would disperse German forces in counter-insurgency operations, maintaining allied morale, while enemy forces suffered from constant, attritional attacks. When the enemy was finally severely weakened from naval blockade, air attack and continuous guerrilla action over years of war, the well prepared and massed British empire forces would be finally deployed in a massive invasion and decisively defeat the enemy. The entry of the USSR and the USA only acted to quicken the pace of this timeline, as it was felt that war between the USSR was an unreliable and unlikely ally given their attack upon Finland, their purges and actions in Poland. Furthermore war between the USSR and Germany was highly unlikely, and while the US entry into the war was highly desirable, it was not possible to base their strategy upon it.

TL,DR Britain's strategy was balanced between winning and surviving the war, and their updated plan can be characterised as an modernised version of their Napoleonic war strategy. Carrying out maritime economic warfare again a land-bound adversary, formenting revolution in occupied nations and rapid amphibious raiding would disperse and demoralise superior enemy numbers, while preserving and gathering British strength until the enemy was so weakened that Britain's comparatively numerically limited (but well prepared) ground forces could be deployed for a knock-out blow.

Sources- I am travelling at the moment, so I am unable to quote directly, however, my argument draws upon the following sources.

P.G. Griffith ‘British Armoured warfare in the western desert 1940-43’ In Harris, J.P., and Toase F.N. Eds., Armoured Warfare (Ellesmere Port, Deltatype Ltd., 1990)

Bidwell S., and Graham, D., Fire-Power (Barnsley, Pen and Sword Books Ltd., 2004)

Buckley, J., British Armour in the Normandy Campaign (London, Frank Cass, 2006)

Buckley, J., Monty’s Men (London, Yale University Press, 2013)

English, J. A., and Gudmundsson, B. I., On Infantry, (Westport, Greenwood Publishing Group Inc., 1994)

French, D., Raising Churchill’s Army (Oxford, Oxford University Press, 2000)

Hart, S.A., Colossal Cracks (Mechanicsburg, Stackpole Books., 2007)

Keegan, J., Six Armies in Normandy, (London, Pimlico, 2004)

Place, T.H., Military Training in the British Army, 1940-44 (Abingdon, Routledge, 2000)