And everything assumes I wouldn't die of random diseases right away.
I haven't read all the posts, but 11th Century London would very much depends on the year. If you get there in the middle of the century you might be able to help Harold Godwinson win the Battle of Hastings. Perhaps defeat the Normans before they arrive as you can tell Harold of the plans of William and the other Harold.
Black Powder isn't that hard to make - There is some potential shock and awe - and stampeding enemy cavalry. The steel to make muskets is pretty far out. But bronze canon and basic iron canon are possible as are all the fun things being produced in
China at the time.
In imagining this sort of thing I'd always thought I'd simply hold the palms of my hands out for all to see. Nobody - I mean nobody older than 4 years old in medieval Europe had hands as soft on smooth as mine are. Clearly I'm nobility of some sort. I'd hope to get sent to the local priest or official and then get passed up the line as each hopes to earn favor with their betters.
Consider that after listening to some Latin spoken, since Latin writing is phonetic one can read from a Latin text even without knowing the meaning. This would demonstrate an education level that supports the nobility presumption. What's more, an ability to read a book even though I don't know the language would be something fairly miraculous I suppose.
And a little knowledge of Romance languages would go somewhere to understanding Latin. Focus on learning local languages.
Perhaps make up a good story for my presence. I am from a kingdom across the Western Sea (Atlantic) where I'm a minor lord of some sort with a tiny retinue of servants, enough that I don't need to lift a hand to do anything, obviously. Maybe I was in a ship that was blown way off course in a storm and damaged and when we hit landfall I was kidnapped. After much misery and uncounted days, and after infighting and calamity among my captors I found myself escaping and running aimlessly through the night only to come to in an alley in London. Boy am I weak after my ordeal.
I am here happy to learn your ways and perhaps share a few things that we do differently, though in our land the nobility learns about work generally so I won't claim to know how to work a forge. But lets calculate stuff - math is my friend. Understanding of modern chemistry. They don't have even basic knowledge of distilling. So many good things to share.
If I didn't die of a random disease or dysentery I might make it.