Yes yes yes, see Les Miz in London. It's still wonderfully fresh, and it's been running for 20 years over there! I'd also recommend taking in a show at the National Theatre, because the productions there are consistently amazing. It's a shame Sweeney Todd has closed, because it was absolutely amazing.
What I highly recommend doing when you get to London is buying the current issue of Time Out (they're released weekly), because not only does it outline the theatre schedule, but it also tells you about other activities, both ones that are only going on for that week and ones that occur regularly (i.e. bus tours and museum hours). It's a ruddy useful tool (hee hee! London speak creeping through). I'd also recommend buying an A-Z guide (they call it an A to Zed), which you can probably get at Heathrow (or Gatwick, if that's where you're landing) and you can DEFINITELY get at any Tesco supermarket. It's this little book that has maps of every street and area in London--it's great if you want to see the city on foot, because it's easy to get lost without a map.
As for Paris, if you're only going to be there for a short time (less than three days), don't even touch the Louvre, because you'll just end up rushing through the place and not really seeing anything. The Musee d'Orsay is a better alternative for a short stay, because it's smaller and the art is not as notorious, but just as gorgeous. Also be sure to take a walk through the Jardins Tuilleries, see the Eiffel Tower (it's absolutely breathtaking), and visit Montmartre and Le Marais (two of the hippest districts in Paris).
And most importantly, have fun and take in the atmos.
"Peace! The charm's wound up."
--Macbeth