london to paris day trip
Yes, I've done it. So has my mom.
Eurostar is the way to get from Paris to London and back. They have decent advance ticket prices, as well as new "snap" fares (that might put you on a train at a less desirable time, but for a cheap fare).
I didn't bother with first class when I went on Eurostar with my daughter, and I brought a nice picnic lunch with a serving of wine for myself (one of the advantages of trains in Europe is that they don't have all the fecking stupid paranoid security rules about liquids and solids).