traveling by metro - Ecole Militaire to Paris Gare Du Nord for Eurostar to London

The route planner on ratp.fr says it takes 31 minutes if you take the metro changing at Strasbourg-Saint-Denis. You may want to add 15minutes as you suggest for a more relaxed trip. I've done that trip a couple of times and would give myself the extra time.

Remember, you have to be at the station at least 30 minutes before the train's scheduled departure. I would leave the hotel around 7 am. Well, actually, I would probably take a taxi.

A taxi would be around 20 Euros to Gare du Nord. Why fool around with the metro and try to cut it so thin time-wise? Get there at 0730-0800, get a coffee and a pastry and then line up on the second level to go thru immigration. Have a pen handy to fill out the customs/immigration forms for the UK. Take along a snack or another pastry and settle in for a nice snooze.

You might get by with a little less than 20€ as I paid about that for a taxi during a Monday afternoon rush hour from GDN to the Rue Cler area. You should have much less traffic on a Sunday AM. I would also plan to be there a bit earlier than 45 minutes ahead of departure.

Keep in mind that the metros run on a less frequent schedule on Sundays than during the week. So you also have to add some minutes waiting at both metro stations for a train to arrive. I would definitely give myself 45 minutes, and in addition, you'll have to find your way in the Gare du Nord once you've arrived. (i.e. the trip time is not equal to the time it takes you to get off your train, follow the signs to Trains Grandes Lignes), come upstairs, and orient yourself to find the Eurostar boarding area and the stairs to get up to it.)

thank you for all the helpful replies

A couple of years ago, our Gite host booked a an early morning taxi to take us to Gare du Nord. Waited for half an hour in the street. Taxi didn't bother to turn up. We had to hit the streets towing bags trying to hail down taxis. Give yourself plenty of time to implement Plan B if you have to.

We have arranged airport taxis a dozen times in Paris and never had them not show; a Plan B is always prudent of course.

I would leave 45 minutes for the trip in any case and aim to arrive about 45 minutes before departure time. I don't like to be rushed and have to worry that any hitch in the process might end up with me being too late for a high stakes flight or train. There is plenty of place to sit in the Eurostar lounge and there is coffee and such available, so you can arrive in plenty of time and have a cup of coffee if you are seriously early.