I will be in London and Paris in October. Therefore, I will probably have a warm thick winter coat and/or umbrella. Do most of the major museums and indoor monuments have a coat check? I'd hate to carry around a heavy coat and wet umbrella during my tour of the museums.
Please offer suggestions...
You'll find most museums have coat check rooms. What other suggestion did you have in mind?
I agree with the previous posters: You will not need a heavy winter coat in October. A wind- and water proof raincoat or jacket with a hood, a (silk)scarf and a pair of thin gloves, a fleece and/or cashmere sweater or top should keep you toasty. You may get warm Indian summer weather, too. The answer is layer dressing; you want to be able to take some things off as well as layer them on top. I never take an umbrella anymore, if you really need one, buy a cheap one when you're there.
I took a one-size rain poncho to Paris in June and it was a godsend. Not only did it keep me dry (it rained and rained and then it rained) but my backpack and camera as well, and I had both hands free. It folds up to nothing and when it was wet and the skies were clear, I just put it in a plastic bag in my pack.
The museums all had coat checks, I don't remember seeing any at the monuments or churches.
