What are suggestions to do in London and Paris in the even that we have rain the entire time we are there? We will be going to all the requisite museums, cathedrals, etc. Do people walk around and go to the parks in the rain?
Whenever I travel, I carry a small six inch collapsible umbrella. Very small and weighs practically nothing.
Why let rain ruin your vacation. Just go.
Don't waste a moment of your vacation because of rain. Plan for it. Bring a rain jacket with a hood and a small umbrella (or you will end up buying a crappy one from a street vendor for big $$)
When it rains, everyone disappears, and it's your time to really enjoy the sights without the crowds!
Londoners are use to the rain. Be a local. Just be prepared.
We bought packable hooded rain jackets from Cabella's and have used them every time we've gone to Europe. They weigh very little, pack small and only cost about $30 each. When it rains, we just carry on.
On our trip in 06' it rained the first 2 weeks out of 5. Our shoes were pretty water proof (NB hiking shoes) and on a whim I had bought us rain pants at ROSS the week before we left. I sure was glad we had them. We walked all over in the rain. If we hadn't we would have missed out on a lot of wonderful things! Just be prepared and make the best of it!
If you're traveling in the UK you cannot let rain stop you. The rain there is different than on a continent. It can be much more changable. A wee mist means full steam ahead with walks. It's only an all day down pour that's ever stopped or slowed down my travel. If you have a true all day down pour and you've exhausted the museums and galleries, you might look for a good pub with fireplace. ; )
We had one day of heavy rain in 06 (summer) and thankfully I had a raincoat and umbrellas with us (small ones). We did end up spending the entire day in museums which was fine with us. As long as you prepared for the rain, you can still do things like even shopping, and leave the better days for parks and other outdoor activities.