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All things being equal, your SEO would not be be affected at all purely because of a host change. Let me clarify the "all things being equal" part: will your new server offer the same performance as the old server? As Cody suggests, if the new server offers better overall performance that would be good, and if it is worse that would be bad. will there be any downtime during the change? Ideally your should be able to make the move with zero downtime. Any downtime would obviously not be good. is your new server physically located in a significantly different location? If your current server is located in England, it can offer better local results for visitors located in England. If you then move your server to the US, your local SERP can be affected. there are many server settings which can impact SEO and performance. These can easily be taken for granted. If you use any form of shared hosting, you should try to thoroughly understand your current settings and ensure you are aware of your new host's settings. Webmasters are often surprised to learn about changes after they have moved.

Now it all makes sense, thanks for the help.