God, doesn't anyone here understand economics.
The pound falls, so goods we export are cheaper, and goods we import are more expensive. The pound initially fell by about 20%, but that doesn't translate into a 20% rise in inflation, because it's the raw goods that cost 20% more, not the final price. The final price is made up of raw goods, transport costs, and profit at several points, so the raw material rise isn't the same as the final store price. In addition, a lot of stores absorbed some of the initial rises by cutting their profit margins. Then the pound started to rise again, so the period that inflation is compared against doesn't cover the same period as the punds fall and then rise. I think the pound has risen against the dollar to close to the rate it was before Brexit (ignoreing the blip to $1.50).
But inflation only went up by 2.9% because it covers a variety of goods and service, some of which went down (oil I think, and mortgages), whilst imports went up, so there's no real short and quick answer to this problem.
But yes, the value of the pound against any other currency, is effectively just a casino, and the governments have no control over it. It's the money markets that either have confidence in a currency, so will buy it, which makes it rise, or they have no real faith in where a country is going, so will sell that currency, and it'll fall. Gerorge Soros actually made the pound fall some time back, by just betting against it, and that caused the markets to react, and it became a self fulfilling prophecy. Coupled with the fact that a lot of stocks and shares are now bought and sold by computers that will sell if a certain point is reached, so that makes a share price drop, and that makes other computers sell the shares, so again it becomes a non stop fall that may not have had any real justification.
If you look at a countries share indeces, you can see seasonal flcutuations that are more determined by holidays and the need for liquid cash at certain times of the year, so the stock market is also driven by the things people do, sometimes more so than what the shares and companies are actually doing.