Our weather here in London can go either way around Christmas. Sometimes it's very cold and other years in can be mild. But in either case, you always see local familes walking around London during Christmas, even with very young children. The streets are safe and very easy to walk around, even with a baby stroller or baby buggy. If you want to treat yourself or you have further to go, take a licensed London Black Taxi (not a mini-cab, which can be unsafe). All licensed London Black Taxis have plenty of room for a baby stroller or baby buggy. They have a special seat belt that can go around the stroller or buggy so you can leave the baby in the buggy-all strapped in and safe. Use only a reliable company such as London Black Taxis.net, which my family always uses when they come to visit.