Side trip from London: Paris or Berlin?

Paris.

Take the Eurostar train which goes from city center to city center. Buy the tickets as soon as they go on sale which is 6 months out for the cheapest prices. www.eurostar.com

You'll be there in a little more than 2 hours so if you have just 3 days you'll be able to maximize your touring time even thought you'll wind up killing a half a day what with travel to St Pancras International in London, getting there an hour ahead to check in and go thru security, train time, then the time from Gare du Nord to your hotel.

Three days will barely scratch the surface in Paris as will 8 days in London, lol!

Speaking as a one time Francophobe, I would definitely do Paris. The travel time is short, it is a beautiful city and there is so much to see that three days will go by in a flash.

In the 2.5 - 3 hours it would take you to travel to Heathrow, go through security, and wait to board a plane to Berlin, you could be in Paris on the Eurostar ( not counting security time at St. Pancras).

Paris!

Reading the other replies, I am almost feeling sad for poor Berlin!

But Paris wins, hands down. Easy journey on the Chunnel, fabulous city to explore, wonderful food, majestic museums, super shopping, and WARM BAGUETTES.

Berlin and Paris are both fabulous. But with only a few days away from London, Paris is much easier, since you can take a fast train instead of a flight.

Tickets for this Eurostar train become available 180 days out. They start out inexpensive if booked in advance as non-refundable and non-exchangeable, and can skyrocket if you wait until the last minute. So, book these as soon as you are sure of your plans. https://www.eurostar.com/us-en/?

Everything you need to know about this train: https://www.seat61.com/London-to-Paris-by-train.htm

London to Paris by train, so easy and fun too. A perfect combo!
Put Berlin on your list for a future trip. It combines well with Dresden, Germany and Krakow, Poland.

My vote is for Paris as it is a wonderful city and easy to get to from London. Leave Berlin for another time as this is also a great city but longer period of time to get to and you want to get to a city quickly when you only have three days.

Regrettably, we have wasted 13 days in Paris & 3 days in Berlin on our travels. We would trade them all for 3 days in Prague, Vienna or Rome.

Regrettably, we have wasted 13 days in Paris & 3 days in Berlin on our travels

Maybe stop going back to Paris and Berlin if you hate them????

Both are great, but Paris is a shorter journey, thus it is the better choice.