1st time to London

1. Impossible to answer with any accuracy. When are you travelling? Carry on luggage or checked? How many other arrivals all heading to Immigration? How backed up is security? Could be under an hour. Could be a lot more. Plus, add an hour to reach the hotel from LHR.

2. You should be able to squeeze in a visit to the British Museum in the afternoon if you have pre-booked a timed ticket. Again, depending on time of travel, it could be very crowded. Usually indoor activities on arrival day are discouraged if you have had a long flight. But if you are arriving from somewhere in Europe, you are unlikely to be jet lagged. Otherwise, try to stay outside. Take one of Rick's self guided walks, like the Westminster walk. Or see if you could take one with Walks of London.

3. You likely do have too much on day 2. Start with the Tower of London and try for a pre-booked ticket and entry time for the official opening. Go directly to the Crown Jewels collection, then tour the rest afterwards. That should take all morning. You could possibly do something in the morning of your departure day. Check out of your hotel, but store your luggage with them. Leave plenty of time to return to your hotel, then get to St Pancras for the train.

4. You need to be at the Eurostar check in line 90 minutes before departure. (3pm). You need to clear security, British Immigration, AND French Immigration.

5. As long as it takes to walk from the train to the exit.

"How backed up is security?"

Security is departures only, not arrivals, so nor relevant in this case. It's just passport control and then walk through Customs.

For arriving at Heathrow, I'd allow an hour max, possibly less. The main delay could well be collecting your luggage. And agreed, allow an hour to get from airport to hotel.

I think day two is very busy, but possible. Maybe drop the Southbank walk and boat ride.

For Paris, as CJean notes, because you've done French passport control at St Pancras, you just walk off the train at Garde du Nord. There's a taxi rank at the station to get to your hotel if that's how you're traveling.

Second Rick's self guided tours. Very informative, and i have been to London many times.

I appreciate your information.

First time I went to London, I did the Hop on, Hop off tour. Something to consider in your short time frame. The Bus will take you all over the place and you can get on and off in your time frame. It will take you to all the high points you mention and more. It’s also a great way to see a lot of the city and get a tour.

Hi! I agree with CJean about your Day 2 plans. Way too much.

If you see the Tower of London, and it takes all morning, maybe just try for St. Paul’s in the afternoon. You could even go to the Choral Evensong service, which is free. You don’t get to explore all over, but you get to go in, listen to gorgeous music, and observe the magnificence of the sanctuary. To get there, walk to St. Katharine docks from the Tower (very short walk) and take the route 100 bus directly to the cathedral. The trip takes 30 minutes (same as the Tube) and you can signtsee along the way, since you won’t be under ground.

Are you arriving on a transatlantic flight? If so, I wouldn't try the British Museum on arrival day, unless you're one of those fortunate people who manage to sleep for hours on the plane and arrive refreshed. I'm usually a zombie by the time I arrive and check into the hotel. I've found that walking around in the sunlight helps to reset the body's clock somewhat.

Are you planning on going in and touring Westminster Abbey and the Tower of London, or are you just going to see them from the outside? If you are planning on going in, then yes I think day 2 is much too crowded. I'd pick one or the other. And then add the Southbank walk and a boat ride. And maybe a walk past Buckingham Palace.

Since your train isn't until 4pm on day 3, maybe you could either go to the British Museum that morning, or do Westminster Abbey that morning (go early and beat the crowds). You'd leave your luggage at the hotel until you needed to pick it up to go to the train station. Most hotels will do that.

I think I'd switch the St. Paul's tour to arrival day, rather than try the British Museum on that day.

Transport for London is a useful government operation which can help you plan your commutes around the city.

https://tfl.gov.uk/

Google Maps offers a similar service, with less attention to prices.