A few thoughts:
1) Swiss flies from Terminal 2. Not the nicest terminal - you don't want to spend a lot of time there. DL does indeed arrive at Terminal 4.
2) I would be surprised if you can't just check your bags all the way through. Simply bring a copy of your itinerary, show it to the agent at check-in, and ask if you can check your bags through to Zurich. I've done this numerous times, with multiple airlines. BA is the only major legacy carrier that I have read about that will often refuse.
3) If DL will check your bags through, then you don't need to collect your bags. Follow the "Flight Connections" signs to change terminals without going through customs or immigration. You can use the connecting lanes without an onward boarding pass, there will be desks at the other end where you can pick up the pass.
4) In the unlikely event that DL won't connect your bags, then you will need to clear passport control (make sure to fill out the landing card), collect your luggage, clear customs, and make your way to the train station. At the train station, take the Heathrow Connect to the Terminal 1,2,3 stop. Bring your walking shoes, as the walk from the Terminal 1,2,3 stop to Terminal 2 is loooong.
Assuming that DL will check your bags through, 2 hours should be enough time (though 2.5 would make me feel safer). If they won't, then it will be tight, and might not be doable if the lines at immigration are long. To that end, does anyone know if you get a Fast Track pass when flying BE?