If I had to guess, I would say that you probably have an especially large mailbox, and so the usual routines Mail needs to do every time a message comes in takes a lot longer.
It is also possible this is an early warning symptom of a bad HDD, but first I would try another email client such as Thunderbird to see if the symptoms persist. If it's just something screwy with Mail, then you can either decide to just dump it in favor of something that works like Thunderbird, or delve a bit deeper into figuring out exactly why it's acting screwy.
Now, if Thunderbird ends up causing the same symptoms, it'd probably be worth taking the thing somewhere to have a diagnostic run on it. It's also possible you just need to upgrade the RAM, because having Quark and Photoshop open at the same time would probably eat up a lot of RAM. It's not outside the realm of possibility that all you're experiencing is some rather extreme swapfile use, but it couldn't hurt to get the system checked out to be sure. Make sure to explicitly specify you want them to run the full 1-2 hour long test on the HDD, not just the 5-10 minute one. If they look at you with a deer in headlights kind of look, politely tell them to just forget the whole thing, take your system, and go somewhere else with it. Apple uses the trained monkey method of hiring, same as fast food places. The idea that you break down complex processes enough that you could train even a monkey to do it. How well does that idea tend to work for fast food places? It works about as well for Apple. So, if you get lucky and the person you talk to seems to know what they're doing, great... You get someone who looks like they're just a few IQ points above involuntary drooling, take it somewhere else.
Can anyone advise us on the following?
We are using a Imac 27" mid 2010, Mac OS Lion.
When an email arrives while working in Quark or Photoshop (and other programs) we leave the program and go to mail to read it. On returning to either Quark or Photoshop etc the program has stopped responding requiring a force quit.
Mail also seems to be running slower than usual.
Any help with this issue much appreciated.