How much firepower did the British navy represent in 1940?

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The land-based regiments would have a lot more firepower. Typically you might be talking several divisions having perhaps 2000+ guns combined. Note however these are relatively small caliber compared to naval guns. Most field artillery is 4-, 5- and 6-inch guns, whereas a battleship would have 8-10 15" guns.

The critical question in a fight like this is not so much firepower, as whether the invader can supply the beachhead. Soldiers need three basic things: water, food and ammunition. In mechanized warfare you also need lubricating oil and fuel. If a steady stream of these commodities does not reach the unit, they will surrender (or otherwise become ineffective). The importance of the navy would be to prevent supply ships, which are very vulnerable to any warship, from landing.

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I have seen it stated that the British Navy would have been at the mercy of German bombers had the R.A.F. not contained them. Germany had a sufficient bomber force in September of 1940 to bomb day and night if required. However if the case of the Americans in the pacific, there was any amount of heavy bombers deployed against the navy of Japan. They proved notably ineffective due to the fact that bombes dropped from the combat operational height would only strike manoeuvring ship by pure accident.

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I was given several pieces of information in another answer that allowed me to construct my own.

First, I was reminded that the typical division of 10,000 to 12,000 men has about 2,000 artillerymen. At the rate of 20 men per gun, that is about 100 guns per division.

It was also helpful to learn that "most field artillery is 4-, 5- and 6-inch guns," because that's the caliber of destroyer or light cruiser guns.

If there were 66 cruisers (heavy and light), there might be eight guns per ship, or the total of about 500 six inch guns, or the equivalent. Each destroyer has about eight five inch guns, and 184 of them will have over 1400 guns. So far, we have enough guns for 19 divisions.

The 15 battlewagons would have about 8 guns apiece, or about 120 guns in total, but of much greater caliber than the field artillery. The radii of each of their shells would be about three times that of a destroyer, and their "throw weight" twenty-seven times that of the smaller shells, based on volume being 4/3 times pi times r cubed. (The first two terms, 4/3 and pi cancel out, so a battleship shell would be 27 times the size of a destroyer shell, based on 3r-cubed. Multiply this 27 factor by 120 guns, and you get the equivalent of over 3000 guns, or the firepower of about 30 divisions.

So Britain's naval artillery power was equivalent to that of 40-50 land divisions. And it would be probably be more valuable than an equivalent amount of land-based artillery because of the "crossfire" effect, and because it is easier to move this "artillery" by sea, than land artillery.

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