OK, here is my report. We contaced lots of Civs, traded, even got in a war!

Don't worry, its nothing much. I also made an extensive map outlining my ideas. Sorry I forgot to put the minimap, but everything should be explained on there with lots of colors and arrows.
[Turn 1 - 4000 BC] I found on the starting spot after exloring with the Scout and the Worker. The Galley reveals some grassland on the island to the South. Scout started in London.
[Turn 2 - 3950 BC] Island seen to the East. The island to the Southwest has a Cattle on it...looks like its good!
[Turn 3 - 3900 BC] We pop Burial from a hut.
[Turn 4 - 3850 BC] The Island to the Southwest looks uninhabited and like it could fit two, maybe three cities.
[Turn 5 - 3800 BC] Nothing. Another island spotted to the far West.
[Turn 6 - 3750 BC] Nothing.
[Turn 7 - 3700 BC] We've discovered the extent of our island. There is a little desert and Plains to the North. Scout changed to Warrior in London.
[Turn 8 - 3650 BC] We contact Russia! We could see their Scout on an island to the North when our Scout was on the tip of our island. We trade Alphabet for Bronze and 10g. We start the Wheel at min sci.
[Turn 9 - 3600 BC] The island to the West is a tiny strip. It would be only worth settling so the city could act as a canal.
[Turn 10 - 3550 BC] Warrior->Spear in London. More islands spotted to the far far West.
[Turn 11 - 3500 BC] Tan border spotted in the far West. We contact the Ottomans and trade Masonry and 10g for Pottery and Alphabet.
[Turn 12 - 3500 BC] Nothing.
[Turn 13 - 3450 BC] Nothing.
[Turn 14 - 3400 BC] Even more islands seen to the West. (I'm only writing this because I don't want to write "Nothing".

) I think we should build a Galley ASAP after a Settler to explore to the much-neglected East.
[Turn 15 - 3350 BC] We find Moscow to the North.
[Turn 16 - 3300 BC] Nothing.
[Turn 17 - 3250 BC] Damn. Russia seems to have a very large island. Grr.
[Turn 18 - 3200 BC] Spear->Settler in London.
[Turn 19 - 3150 BC] Nothing. Our galley is nearing its way to our home island now.
[Turn 20 - 3100 BC] The Ottomans start the Collosus.
[Turn 21 - 3050 BC] Our Galley reaches the home island's northern tip and goes to explore the East.
[Turn 22 - 3000 BC] Nothing.
[Turn 23 - 2950 BC] We do a straight trade, Code for Masonry, with Russia.
[Turn 24 - 2900 BC] Nothing. Mountains seen on the Eastern Island.
[Turn 25 - 2850 BC] Settler->Spear in London. We contact Spain on the island past the Mountain Island.
[Turn 26 - 2800 BC] Nothing. Spain has two cities, and that looks like all they can fit on their main island.
[Turn 27 - 2750 BC] Nothing. An Ottoman galley appears by our island, lets hope its unoccupied. Speaking of that, we have to get a foothold on the western island as soon as possible, hopefully after the second city is founded. IMO, the third city should be on a second island and it should have a worker with it, this way it can develop on its own and colonize the rest of the island by itself.
[Turn 28 - 2710 BC] What's this? An Ottoman Warrior is dropped off on our island. He doesn't want to fight, does he? We have a fortified Spear in our territory, lets hope it holds up, eh? I tell him to withdraw, and he gives some excuse. Strange. We'll see what happens.
[Turn 29 - 2670 BC] They declare war, we kill the Warrior without taking a scratch. Heh. His pitiful attempt at wiping us out early failed. Even if he had succeeded, we have a second settler in place to simply rebuild London. It would be a setback, but not death. York is founded.
[Turn 30 - 2630 BC] Pink AND Purple borders seen on an island to the far East! Nice.
[Turn 31 - 2590 BC] We contact the Vikings. It is apparently two islands that are very close. Spear->Galley in London.
[Turn 32 - 2550 BC] Nothing.
[Turn 33 - 2510 BC] We contact the Chinese. We now know 5 Civs, and we have a corner on the tech market.
[Turn 34 - 2470 BC] Nothing.
[Turn 35 - 2430 BC] Nothing.
[Turn 36 - 2390 BC] Nothing. We're going to use our starter galley to hop to an island that is three turns across the sea, far to the East.
[Turn 37 - 2350 BC] We make it. Duh.
[Turn 38 - 2310 BC] No inhabitants yet. Its all jungle so far.
[Turn 39 - 2270 BC] Spear->Settler in York.
[Turn 40 - 2230 BC] Galley->Worker in London. That's it for me.
[Notes] OK. The next settler should definetely go to the island that is closest to us in the West. Please take the Settler/Spear from York to go to the Western Island, and take the Worker from London on a second trip to bring to that island. So, in the end, we should make two quick trips to the island and drop off a Settler, a Spear, and a Worker. Besides that, I think we should take complete control of our island and the Western Island and continue to explore. After that we can decide which island to take next. I don't think it will be empty though, so an early war may be necessary.
EDIT: File upload isn't working. I'll attaching the zipped save in this post, and the map (its a longshot) in the next.