Why does the brittish government need permission to start a general election?
Well, because a previous Conservative government passed a law that makes it so. This was a demand of the Lib Dems when they went into coalition with the Tory party in 2010; the relevant section is Section 2, which mandates that early parliamentary elections can only happen when 2/3rds of the Commons votes in favour of them. This law, like all law, can be amended with a 50% +1 majority instead of course.
Why would the opposition be the ones who say when the current government stops working?
They're not. The government doesn't stop working because they can't get an election; they have a vast swathe of executive power in addition to their ability to make legislative changes through Statutory Instruments and so on. They can govern just fine, they just can't pass new laws very easily.
Wouldn't this result in a non-working state?
Good god no. Even if government shut down entirely; countries routinely go for lengthy amounts of time without functioning government. This mostly happens after general elections, when political parties are in the midst of negotiating a coalition agreement. When all is said and done, the Civil Service can run a country just fine for a really long time.
When a government has a fallout and no longer feels the motivation to continue, the lower house can prevent an election. But at that time it also means the government (since they felt they cannot continue in the current state) might refuse to do any "governing".
Creating a deadlock.
What happens if the government actually states "well we're no longer continuing"?
No policies are changed, laws aren't kept up to date through Statutory Instruments in the usual fashion, but Parliament could pick up that slack I suppose. I guess foreign policy would be the area that would suffer most heavily. The Civil Service keeps the country ticking over under the existing laws and policies until either the politicians resolve whatever political problem is preventing the opposition from calling an early election and/or the government remembers they're adults and goes back to governing. By and large; no big deal.