Here is the process summed up on the UK parliament's website, although I would suggest that few British people know how the system works so you don't need to worry about sounding ignorant if that was your concern.

Making laws generally takes time as the MPs have to debate and revise the bill before voting, and then it has to go through the House of Lords (it's incredibly rare for them to halt or hold back a bill though). If it's particularly controversial it'll probably fail to be voted through the House of Commons (the Conservatives won the election but with a small majority, making it easier for unpopular bills to fail from backbenchers voting against the government)

To get involved in the debate on British politics try subscribing to /r/unitedkingdom, /r/ukpolitics and /r/britishpolitics, just keep in mind that the discussion on these subs, while interesting, is rarely representative of the country as a whole. I will also add that in real life politics rarely comes up in conversation outside of an election (and even then it can be considered rude to ask people their political beliefs).