There was no British liveline in the Mediterranean :the British liveline was the Atlantic .
I suggest that you visit your library and go to the WW2 History section. How was Malta supplied if sea convoys didnt sail in the Med? And how exactly could convoys from the Atlantic suddenly appear in Malta without sailing the Med? Even the top boffins today cannot pull off a miracle. I think your watching too much Star Trek
Here are just a few examples:
September 1940 – Operation*Hats
The Mediterranean Fleet escorted a fast convoy of three transports (carrying 40,000*short tons*(36,000*t) of supplies including reinforcements and ammunition for the island's anti-aircraft defences) from Alexandria and collected another convoy from Gibraltar. En route, Italian airbases were raided. The*Regia Marina*had superior forces at sea, but missed the opportunity to exploit their advantage.
October 1940
The heavily-escorted Convoy MB6 from Alexandria reached Malta safely. The escort included four battleships and two aircraft carriers. An Italian attempt against the returning escort employing destroyers and torpedo boats ended in the*Battle of Cape Passero, favourable to the British.
November 1940 – Operations*Judgement,*White*and*Collar
A supply convoy from Alexandria arrived safely, coinciding with a troop convoy from Gibraltar and the air attack on the Italian battlefleet at Taranto (Operation Judgement).
Twelve Hurricanes were flown off*Argus*to reinforce Malta (Operation*White), but the threat of the Italian fleet lurking south of*Sardinia*prompted a premature fly-off from*Argus*and its return to Gibraltar. Eight of the planes ran out of fuel and ditched at sea. Seven pilots were lost.
A fast convoy sailed from Gibraltar to Malta and Alexandria (Operation*Collar). It was attacked by the Italian fleet at*Cape Spartivento. All transports arrived safely.
January 1941 - Operation*Excess
Operation*Excess*took place — a sequence of simultaneous supply and empty return convoys between Malta and Gibraltar and Alexandria. The transports arrived safely with 10,000 short tons (9,100*t) of supplies, but the*Royal Navy*lost a cruiser (HMS*Southampton), with another cruiser (HMS*Gloucester) and an aircraft carrier (HMS*Illustrious) badly damaged and a destroyer damaged beyond repair.This was the first action to involve the*Luftwaffe. The Italian torpedo boat*Vega*was sunk in the course of the operations.
May 1941 – Operations*Tiger*and*Splice
An urgent supply convoy from Gibraltar to Alexandria (Operation*Tiger) coincided with reinforcements for the Mediterranean Fleet, two small convoys from Egypt to Malta,*and 48 more Hurricanes flown off HMS*Ark Royal*and*Furious*(Operation*Splice).*The only loss was the 9,200 long tons (9,300*t) cargo ship*Empire Song, which hit a mine and sank with a cargo of 57 tanks, 10 aircraft and several trucks.
Tiger*was transporting tanks (Matildas*and the new*Crusader tanks) needed for the operations in North Africa, these had been intended to be sent via the Cape but were diverted via the Mediterranean. Over 200 tanks reached Alexandria on 12 May.
The Luftwaffe transferred much of its strength from Sicily to prepare for the*invasion of the USSR, relieving some of the pressure on Malta.
The Malta-based submarine*HMS*Upholder*attacked and sank the large Italian troop transport*Conte Rosso.
I suggest that you do a bit more research.
The outcome of the war in NA was not determined by a supply war,it was determined by the British superiority:in 1941,the strength of the Africa Corps was some 30000 men,at the end of 1942,it was even less .Even if all the supplies that arrived at Tripolis,were going to Alamein (Tripolis to Alamein =2000 km),the Germans still would loose .The outcome of the war in NA was known beforehand.
Every battle fought right from the beginning of time relies on its supply lines. Without supply lines there is no fuel, no food, no ammunition, no fresh troops or other supplies to the front. One of the major worries regarding D Day was the problem of supply, which led to the design and construction of the floating harbours.
The British defeat in Singapore was partially caused by the inadequate supply of modern aircraft and other equipment. The Chindits in Burma only managed to do what they did because of supplies dropped by air.
As a matter of interest, supply units suffer extremely heavy casualties from enemy air and artillery attacks because they are so vital to front line units