There are four official swimming strokes: front crawl, back crawl, breaststroke and butterfly.
Front crawl is generally the preferred stroke for open water swimming as it has the least resistance in choppy water. It is generally the fastest stroke and is used by elite open water swimmers. Breathing can be on either side, which can be useful if there are waves coming from one side.
Breaststroke is preferred by some people who dislike to put their head under water, you can also see which direction you are swimming as you breathe, and it is often the only stroke that some people have learned. However, there are a number of downsides to breaststroke: it generates a lot of resistance when swimming; some swimmers find breaststroke hard on the knees over a long distance; if you are wearing a wetsuit your legs can float too high for an efficient breaststroke kick; and if the water is choppy you can get a mouth full of water when you breathe.
Backstroke isn’t recommended in open water as you can’t see where you are swimming and you may end up swimming into other swimmers.
Butterfly over a long distance is only undertaken occasionally by very experienced swimmers. In a mass participation event like Swim Serpentine, butterfly swimmers need to be careful of other swimmers around them as the arms tend to fling wide with this stroke.