A question I often see asked is "Why didn't the British use the 3.7" AA gun like the German 88?". By that they mean why not crank its elevation down to 0 degrees and start knocking out tanks. This is partially supported by Wikipedia's entry on the subject that reads:

"The 3.7″ was inherently unsuitable as an anti-tank gun. It was big and heavy, 2 tons heavier than the German 88, making it tactically unsuitable for use in forward areas. Additionally, heavy AA Regiments equipped with the 3.7″ gun were relatively few in number in the field army and controlled by Corps or Army HQ, or at even higher level HQs, and command of them was not often devolved to the commanders at Divisional level where the anti-tank role might be required."

The implication is that the 3.7" AA gun was only ever used in desperation before being overrun. As you might guess this isn't entirely true. Certainly pre-war, up until some time in 1938, crews were trained in direct fire roles. However the rapid re-arming of the British forces meant that this training was dropped. The mounts also had a part to play. With the MKI being a complex piece of equipment, the gunners faced forward. In the MKII (the static mount) the gunners were facing in towards the gun mount, and finally in the much simplified and lightened MKIII mount the gunners were facing towards the rear of the gun.
In the early years of the war the 3.7" did fight against German armour but not entirely successfully. In part this is because of the lack of suitable ammunition. In most cases they used a plugged shell, which is a shell with the fuse removed. At Boulogne the 2nd Heavy AA Regiment knocked out two attacking Panzers in this manner. Equally at Calais, at the Oyez farm four 3.7" AA guns of the 6th Heavy Anti-Air Regiment were dug in as part of the strong point. Two were sited to cover the wide open ground, and two were sited for AA work. The position was one of the last to be captured by the Germans, although some reports indicate the two forward guns sited for ground defence may have had to have been abandoned earlier, but they did take out several German tanks before being made unsuitable for use.

During and immediately after the Battle of Britain, defence of the home islands was on the minds of everyone. One of the worries was the new 100 ton tanks the Germans were thought to have. The answer was obvious, the 3.7" AA gun was about the only piece the British had that could dent these imagined monsters. So on the south coast a study was undertaken to find which beaches were suitable for landing these super heavy tanks, and several guns were sighted to deal with any landing.

But what to fire? Again here I can shed some light on another dark spot in the historical record. Up until now the only figure for penetration I've been able to find is from British & American Artillery of World War 2 by Ian V. Hogg. He gives a penetration figure of 117mm at 1000 yards against 30 degree sloped plate.

The quickest option was to make an semi-armour piercing round. This SAP round was an normal HE round with an armour piercing cap on top of it. Against a 30 degree slope this would go through 110mm at 400 yards and 94mm at 1000 yards. By July 1941 1000 rounds of SAP had been manufactured and shipped to the Middle East. However a full armour piercing round was under development at the same time. It was, unusually for the British, an AP round with a bursting charge. The British didn't tend to use bursting charges in AP rounds due to the chance of the charge being ejected from the shells base upon impact, making the hit ineffective. Its performance in the documents are 126mm at 400 yards and 115mm at 1000 yards, which tallies nicely with the previous figure. In total one third of a million of the AP rounds were manufactured.

The other innovation that came out of the invasion defence came from Birmingham. Under a plan codenamed "BARGAIN scheme" HAA units were tied into local artillery control and could be used to fire bombardments at pre-arranged targets. This did meet with some resistance from AA command as they pointed out that the high velocity would hamper indirect fire. However it was in this role the 3.7" was normally used throughout the war, where its long range was considered very useful.

Now what of that shipment to the middle east of ammunition? Well it may have first came into use in May 1942, when four guns were dispatched to the Knightsbridge Box at Gazala. The small size of the Box meant that only two guns were accepted into the position. These were set up, but ultimately didn't perform too well.

Things were different at Tobruk when in June German armour assaulted the line. Upon receiving warning of the attack the 3.7" crews dismantled the walls of their dug outs so they could depress their guns low enough. The German tanks were spotted at a range of 1500 yards, but before they could be taken under fire they entered dead ground. The dead ground led right up to the guns, meaning they'd next appear at a range of about 200 yards.
The gunners held their fire and waited. Then the Panzers appeared. The crews lept into action. With the gun barrel so low to the ground each blast kicked up a huge amount of dust, so it was difficult to see what was going on. However with a rate of fire of around twelve rounds per minute the guns laid down a fearsome barrage. In an engagement lasting two and a half hours the Germans were forced to retreat, losing six of eleven tanks that attacked the position.

Elsewhere in the desert the potential of the 3.7" was being tested with HAA units practising AT work at ranges filled with the hulks of knocked out Italian tanks or practising movements to form anti-tank screens. One particular exercise sounded very dangerous as the guns were not unlimbered first and were fired still on their wheeled carriages.

There is one other notable story from the war. During Operation Market Garden there are reports of a battle between Jagdpanthers and a HAA troop near the Town of Veghel, which the HAA troop won.

Image credits:
ww2incolor.com, crusaderproject.files.wordpress.com and en.wikipedia.org