The literal meaning of this video is actually quite harder to see than the deeper one just because the literal meaning is well... quite silly. Once you get past the rather cheesy laugh track, the video is saying that there is a government ministry that is devoted to the creation of silly walks. This random unnamed citizen wants to get a grant to develop his silly walk even though according to John Cleese "The right leg isn't silly at all and the left leg merely does forward aerial half turn every alternate step". The unnamed unsilly citizen then explains "With government back I think I could make it quite silly." Then that leads Cleese's character, who is also unnamed, into a rant about how "Last year the government spend less on the Ministry of Silly walks then it did on National Defense." Then keeps ranting about how other countries have better silly walks then their country does. In short these video is about a guy trying to obtain a grant from the Ministry of Silly Walks to further develop his silly walk. All in all the literal meaning is extremely literal and... silly.
Moving right along the deeper meaning of the video is that governments waste a ton of money on worthless, silly programs that don't help the people of the country in any way. Also that the government gives out grants to develop the silliest ideas, like in the video, a silly walk that isn't particularly silly. John Cleese is playing the character of an upstart person in the silly program that believes that the government should be spending more on the program. You can see these when Cleese is telling the other guy that out of all the ministries that the government has they spend the least amount of money on silly walks even though it is the "most important of all the ministries". Also it's poking fun at the fact that a lot of the money governments spend is in trying to out do each other. When Cleese is talking about the grant he is also brings up the various silly walks that other countries have developed and how comparatively their country is lagging behind. Though I do love space and NASA, it is like the Space Race because there was very little scientific value in sending man to the moon because a rover could do the same and would be a lot cheaper. The reason we did though is to stick it to Russia and prove that we were "superior". I rather like the deeper meaning of these video and believe that it applies to most governments not just the British one (which I'm assuming they are making fun of considering that Monty Python is British)
