London to Paris on Eurostar is only 3 hours, including the recommended 30 minute check-in.
It’s four hours at least, accounting for waiting time and transit time from/to where you would otherwise be, and that’s one way. Out of at most thirty hours total visit (and ten hours a day tourism is knackering).
I had high tea at Brown’s in May for my birthday. Divine. Go. Brown’s is tucked away on a side street, so little riff-raff. Be warned there is a doorman who will open the cab door for you and don’t get out of the cab like I did, with legs and arms flailing and skirt all mussed. The tea room is small and is a mixture of 175 years of tradition and modern decorating and it works. The bar is really cool.
I still think of the dozen tea sandwiches (and scones with clotted cream and strawberry jam, and little pastries) I ate that day.
Do London or Paris, not both.
Do Paris, definitely Paris. London is great and I love it there but Paris is after all Paris.
Of course you already bought theater tickets in London. If you are there on Saturday get up early and head over to Buckingham Palace for the changing of the guard.
That is sort of the point.
I have been to both Paris and London before.
I am taking my GF for her 50th birthday. She has been to Europe only once and that was for a business trip and near zero sigh seeing (Switzerland). In short, she practically never travels. Even her domestic travel has been very slim.
Even for myself my opportunities to travel to Europe relatively few and far between. I have been several times but it is a decade usually between trips.
As a result I felt this may be the one and only time we get to Europe and I really wanted her to see both London and Paris.
I wish I had more money and more time to spend in both places but alas it cannot be so barring winning a lottery in the next few weeks.
Also, reservations are made. It is a done deal so bad idea or not it is what I am in for.
As for the Eurostar we are taking an early train and will be tooling around Paris by 11:30a after dropping bags at hotel so not a lot of lost time. Flying home from Paris so no more lost time traveling. Besides…I consider the Eurostar trip part of the fun and adventure.
Sure. I have no objection to it, as long as tourists know that it is just a superficial theme park version of the cities in question. I appreciate the idea of travel as part of the experience, but that wears off quickly in the case of the Channel Tunnel rail trip, which is rather dull. (Fields. Business parks. More fields. Darkness. Darkness. Darkness. More fields. Paris.)
If I could only go to one place in each city it would be Hampton Court Palace in London and Versailles in Paris.
Versailles is great but it isn’t really Paris, it’s kind of outside of Paris and requires a complete day to do correctly.
If I could only do one It’d be London, Paris has beauty but it has nowhere near the vibrancy and excitement of London. London is cheaper to keep yourself entertained too and unless you are looking for sheer numbers of Michelin stars the food is every bit as good and the choice even better.
And the same for Hampton court.
I think you’ll have a great time. A few days will only give you a taste of each city, but so what? Not every visit has to be about deep immersion. It’ll be worth it just to see the Mona Lisa (terrible, fwiw), Buck House, the tube, etc, as a shared experience with your GF. 
The Mona Lisa was a big let down because you can’t get close enough to it to really appreciate it. That and in my opinion its over hyped and over rated. Definitely check out the Louver but don’t get worked up about the Mona Lisa. You’ll feel better about spending your time checking out Monet’s Water Lilies, trust me you will.
Even if you get only two hours in the Louvre, you can see dozens and dozens of cool things, sculpture, jewelry, mosaics, paintings, mummies…
Before you leave rent Paris, je t’aime it’s a bunch of short stories by different directors and actors about love, filmed in Paris. Steve Buscemi plays a tourist in the Metro who makes eye contact with some lovers across the rails, so funny!
One other tip,
Walk through Trafalgar Square, into the main entrance of the National Gallery and once up the stairs turn right. Through there lay wonders upon wonders, Monet, Van Gogh, Renoir, Turner, Constable, Seurat, Pissaro, glories upon glories in only a few hundred square meters. The big guns cleverly interspersed with lesser known geniuses, but geniuses nonetheless.
It is my favourite museum space in the world and all free…!
Sure you can then move on and take in a Titian or two but gorge yourself on the 19th Century first.