I'm afraid you may have a problem on your Sunday May 1.
Are you arriving in London that morning from France, or are you waking up there?
The usual advice is to arrive at The Tower of London first thing in the morning to beat the crowds and have a decent chance of getting into the Crown Jewels exhibit (included) while it is still quiet. You stand on a moving travelator which takes you through the exhibit so if you are early you can often go out and back in again and get another ride through, That won't be possible if the quick to build up queue has already formed.
Then after the Crown Jewels, back down to the moat near the entry to catch a Beefeaters Tour (included) which then takes you with a degree of military drama (the Beefeaters are all long service ex-serving military women and men) through a number of stops, then you are free to wander the Crown Jewels (for those who didn't make a beeline there first), the White Tower, the Ravens and all sorts.
I worry that you may be late, maybe tired, arrivals. I worry even more that you have chosen the Sunday of the Early May Bank Holiday. The place will be absolutely heaving that day, mostly with families with kiddoes. It worries me that you might not have the most pleasant experience which would be a shame.
About the Changing of the Guard. Did you check that it is on on that day? Also, are you doing that because you want to or because you think you should? It is a very crowded very short event which needs you there well ahead if you want any chance to see anything, especially on a Bank Holiday...
In my opinion a better Changing of the Guard is the Changing of the Horse Guard in Horse Guards Parade. Shiny breastplates, horses, up close, no crowds - what's not to love?
I'd avoid the May Day far left and far right mobs attempting to bring down capitalism in the City single (or mob) handed. If you see trouble it is best to go the other way. Happens every year, although with us effectively at war with Russia now who knows if there will be pro-communism or pro-anarchy mobs this year. In addition to banks and jewellery stores as targets, often multinational places like McDonalds and Starbucks are in the firing line...