As mentioned above, the "rifle shortage" legend came from two sources:
(1) Churchill's plan to try and arm every household in the country. This led to the famous call for US civilian weapons to be donated - which has strongly reinforced the "defenceless UK" myth on that side of the pond. Almost immediately, it was realised that there was essentially no chance of an invasion, and arming the civilian population would not be a good idea - so it was dropped. When the thousands of US donated weapons turned up months later, they vanished - probably discretely into the smelters.
(2) A figure of 90,000 rifles lost, as used in Churchill's statement to the Commons at the end of Op Dynamo. However, it is clear that this figure was just someone's wild guess - at the time of the Commons statement, there was no way that a full audit had been carried out of all the troops and returned stores scattered across UK. Research now shows that (a) the vast majority of evacuated troops were infantry, who came off the Mole fully equipped with their rifles (b) the ordnance stockpiles in France had mostly been evacuated prior to the troop withdrawal, including all of the small arms reserves. Probably no more than 40,000 rifles were lost, and maybe even just a fraction of that amount.
UK war production was so powerful that all of the France losses (tanks, artillery, vehicles, machine guns, radios, etc) were replaced in just two and a half months.
In June 1940, the Germans had no sea-lift, no naval supremacy and no staffed invasion plan. UK already had three fully-armed divisions ready to counter the invasion, and up to a million more men in partly-armed or rearming divisions.
By September 1940, when the Germans had organised a pathetically inadequate invasion fleet, UK had about seven fully armed divisions waiting.
In both June and September 1940, the RN had around 80 fast units on invasion defence. I don't think anyone now thinks the Germans had any invasion chance beyond a doomed airborne bridgehead on the Dover heights (now also shown to have been covered by planned defences).
Interesting photos:
AFAIK, not so far identified - but appear to be returned British troops at Ramsgate or another small south coast port.
Some interesting points:
1. The troops appear to be happy and relaxed, and all bunched together. This presumably means they are on British soil;
2. They are all armed with their rifles;
3. Not only do they have their own rifles, but it seems that they have brought back hundreds of salvaged rifles;
4. The RASC oik dealing with the spare rifles is carrying out a quick unload drill - dumping out the magazines, and working the bolt.
These photos are some of the evidence that shows the BEF brought back very large amounts of equipment that legend had assumed as lost...