Well, taking them from the top:

Brits don't call the hat a derby; we call it a Bowler, so the issue doesn't arise. If speaking of the town or the horse race we pronounce Derby like Barbie.

Titfer comes from rhyming slang - tit for tat: hat, hence titfer. By the way, I'm sure this is generally known, but just in case, despite Hollywood's portrayal of London, very very few people use rhyming slang in normal conversation, it is usually done for fun, so if you visit London, don't expect to need to use it! Of course, you know what taxi drivers are like - they sometimes feel obligated to live up to their image!

Clerk is pronounced like 'ark' (generally, but there is some transpondial drift taking place).