Regarding how long you get to cross the road in London, I can assure you there's enough time as I cross with my daughter in her buggy every day and never have to rush, especially in central London where the timing has been set for crowds to get across safely.
Another top tip is to look on the road at crossing to see which way the traffic is coming from. Look Right and Look Left are painted at all major junctions. It is easy to get disorientated so these instructions are actually really useful.
In all honestly, traffic goes pretty slowly in central London so you won't need to worry. Follow everyone else and you'll be fine.
You can find out more about Road Safety in London and the UK from the Transport for London website where, along with Zebra crossings, you can learn about Pelican crossings, Puffin crossings, and Toucan crossings!