There are tonnes of internet cafe's in London so you should be fine. Just remember to stick to public areas and away from the parks at night and you will be fine. Do you have a place to stay, youth hostel or something?
If you get stuck for anything there are a tourist information places dotted around so they should be able to help you.
If you get stuck for anything there are a tourist information places dotted around so they should be able to help you.