I've not heard of a cottonwood. Some British trees are a danger if planted too close, but not all of them. For example, a silver birch next to the house will probably be harmless whilst a cherry tree planted 15 ft away can uproot your foundations.
Well. Besides being in Oklahoma, and Jayme know this best, our weather at some point will knock it onto the roof. But the roots are what concern me. Cottonwood trees are trees that are a tree that seed cotton. They are a mess.
Cottonwoods populate much of the streambeds and watercourse banks throughout arid portions of the North American continent. They grow in non-arid regions, but tend to get squeezed out by other species which do better with extravagant moisture. I'm not real familiar with the developmental propensities of cottonwoods, but at ten feet, I have my doubts as to its abilities to do much damage....but if you are concerned, most definitely, take it down. No, it does not 'seed cotton', but is called 'cottonwood' because the seed pods are carried on the wind by fluffy matter which looks cottony, but isn't and serves to lift the seed on the breeze. Although a tiny bit of a mess, the cottony mass tends to biodegrade very quickly (if you want to see a mess, try a black mulberry tree...a source of food for silkworms). Given their water-seeking nature, I suspect that cottonwoods are exceedingly stable on their roots which tap deeply for water...but, they could be brittle (like most 'fast-growing' trees, like Silver Maples, for example).
Now, I'm sitting next door to an English oak which has been planted some four feet from the back of the foundation of the neighbor's garage. At maturity, the oak could top out at 80-110 feet tall, with lower limbs extending 60-70 feet. The acidic leaf fall from this will accumulate on the garage roof and degrade the composition roof shingling. The trunk could continue to expand until it stresses and damages the rear wall of the garage. But, those are not my concern...Since the damned thing is just east of the southeast corner of my tiny urban lot, that huge tree has the potential to actually blot out the sun on my back yard....signalling the end of being able to grow tomatoes, basil, herbs, strawberries, roses, delphinia, rudbeckia, honeysuckle, grapes, or jasmine. Although initially it will block out only morning sun in spring and early fall, it's continued growth means my property will become a dark desert under the leaves on its outstretched limbs. Any possibility of access to solar power for my home will be foreclosed for the foreseeable future...thanks to the life of the English oak nest door.