Gunpower is not so much an issue, as there were still plenty of older army type howitzers of around 105mm available as well, whcih could be either on mobile towed trailers, or fixed on either ground, or boat. The heavy type of artillery, needing more elaborate platforms were therefore irrelevant, as makeshift firesupport was more than enough, if the operation was not to be stalled for too long, (at its latest in end summer 1940). There would otherwise be too much defenses, if the British were allowed time to strengthen their lines in the UK.
Most firesupport would be comming from above, since the coastline regions had to be under Luftwaffe controll first, or no landing would take place to start with. With controll of the skies over the landingerea's the Army could ferry across the Channal and land there, under cover of the ever present Luftwaffe and local Kriesmarine light forces, who were primarily top be tasked to defend the convoys against both surface and submerged attacks, as well of minesweeping. Long range railwayguns would occasionally engage whatever targets of opportunity on the British coastline.
British defenses were pretty weak, so shortly after the Dunkerque retreat and the British Army needed time to recover and rearm, which was not the be allowed by the Germans, if they wanted to have succes. Most amryunits of the British were underequipeed for a long time to come and the coastal defenses were still not fully build up. (The two heavy 14 inch guns, taken away from HMS Duke of York, which would be replaced by two additional ones form her delayed sisters, would not be installed and made operational for several months.) Most coastal fortresses were equipped with poorly equipped older types of heavy artillery, mostly lacking all sorts of infrastructure to make them wortkable in some fashion. Besides that, the coastal fortresses were vulnerable to attack from the air, as they lacked the needed heavy bunkers, as seen much later on the French coastline.