I think just like the Normandy landings, unless you can repel an invasion very decisively and quickly the difficulties in winning against the invader with any weapons, mount very quickly. But I truly cannot see the British command allowing the use of gas or chemical weapons where their own civilian population, gas masks or not, would be potentially affected.
The plan by the summer of 1940 was to fight delaying action on the beaches, holding the Germans as long as possible and not allowing a substantial lodgement to develop. This is where gas was considered particularly useful. This would then allow mobile forces to be concentrated against the German beachheads. The planned use of gas was limited to these beachheads where relatively few civilians would have been affected.
Compare Sealion and Overlord and look at the lengths the Allies went to in order to prevent any concentration of German forces against their landings. The Germans didn't really have any comparable plan and their reaction was confused and delayed anyway.
At the same time the Royal Navy, who would have seriously dropped the ball by allowing the landings to happen at all, would interdict the re-supply of any forces landed, cutting them off and allowing the Army to deal with them.
By September 1940 Britain was nowhere near as defenceless as some popular mythology would have us believe. The Army had substantially reorganised and rearmed. In August 1940 there was far more than the RAF standing between Hitler and his invasion of Britain. At the beginning of June the British army had 600 field guns, by August 1600, plus another 820 American 75mm guns, which had arrived with another 200,000 rifles, 2,600 'tank machine guns' (?) and 60,000 Thomson sub machine guns. In three months well over a million rifles had been imported from Canada and the US, equipping the LDF/Home Guard. The regular army had over a million SMLE, plus 75,000 in depots, 65,000 under repair and BSA was turning out 2,000 a week. 400 million rounds of .303 ammunition were to hand. By the end of August Home Defence formations were generally at 80% of their establishment. There were 250 medium and heavy guns with these troops compared to just 140 in June. The supply of two pounder anti tank guns had quadrupled, that of the BOYS anti tank rifle and the Bren gun doubled. By early September the army had 1200 British made tanks, 720 in front line service, including 360 infantry and cruiser tanks and 300 light tanks. Transport problems were somewhat alleviated by the requisition of just about every corporations bus fleet. According to Ismay the total strength of the army in Britain, including men from the Dominions was 75,945 officers and 1,758,122 enlisted men. Brooke, in his own front line, could muster 26 Divisions, 2 of them armoured. By mid-September the Home Guard numbered 1.5 million men, average age 35 (not 95 as some seem to believe, I blame Dad's Army) most now properly armed, uniformed and with some training. Some of these units were very good, others not so much. Colonel Watson of the Durham Light Infantry recalled that the Home Guard in the West Country where he was based were
"extremely good. They all wanted to cooperate with us and we got them on a very high footing. My view was that we should not turn them into Grenadier Guardsmen, but should instead exploit their own ingenuity and individuality."
He might have added local knowledge.
Because of the growing strength and confidence, many of the fixed defences were dismantled inland. They were seen not as a bulwark against attackers but as hindrances to the mobility of Home Forces. Work on the inland 'stop lines' ceased and plans for demolishing bridges etc along the main lines of communication suspended. The only place where fixed fortifications continued to be developed was the beaches and surrounding areas.
There may have been an invasion fever, but not an invasion panic. The growing confidence of the British is reflected in the communiques sent back from various embassies to their respective governments, most importantly to Washington. Even the Soviets conceded that any invasion looked like being a far from foregone conclusion.
In June 1940 the British feared what would happen if any force, even a large raid, was mounted on their east coast. By September those that even believed an invasion could be attempted (a diminishing band) were far more confident that it could be dealt with.
Cheers
Steve