First, go throughout all of Hyde Park and make sure you picked up every single quest. Some NPCs are tucked away. In particular make sure you finish all of Ms. Marpley's quests.
Next, if you don't have any outstanding Hyde Park quests (or if you can't get into Hyde Park yet!), check around other areas - it's possible you may need to talk to someone in Digmoore Station or at the Museum before you can get back on track for Chelsea Court. In particular, check in with Tracy Castleton and Sherlock Bones in Digmoore, and also check the guy inside the Marleybone Museum.
And finally, if none of that works, check inside all the shops and post offices in Marleybone Square. A couple of the main quest-lines send you into those areas (and from there you are sent back to Wizard City or Krokotopia!), so you may have set a quest aside without realizing it was important. If any shop-keeper or postman has an outstanding quest, that might be the one you needed to finish.
Just stick to the main quest in Hyde Park until you complete it. Once you finish the main quest in Hyde Park then you unlock Chelsea Court since its the next area. Once you make it into Cheasea Court then you can complete all the other sides you have involving Chealsea Court.
You could also ask a friend who already completed it to allow you to port in, but that might be time consuming if you have to keep porting to the friend everytime you need to re enter. I would say the best thing to do it finish Hyde Park first, then you can get all the other quests finished after.
When I quest, I try to pick up all the side quests in the world I can get to as soon as I get there. Then I do them as I advance through the main quest. If Im in Hyde Park I do all the Hyde Park side quests, once I move into Chelsea Court then I work on those. It makes things go smoother in my opinion since some of them have the same goals of defeating a certain enemy. Goodluck in Marleybone!