I've only really seen it effect one customer. I'd leave the account active on the old host for a few weeks just in case. That customer lost a lot of traffic at first but then in about two weeks it was back. But I only saw it that one time and that's been several years ago. Seems like the old hosting was shut down a few days before the site went live on our servers. But if that's your main source of traffic better safe than sorry.
I'm using a hosting company based in Sweden now.
I've decided to change to Site5 using their UK server as most of my visitors are from Europe.
Will this move affect my SEO in any way ?
In regards to your question, the short answer is that it probably will not effect your Seo. Nevertheless, as somebody has already pointed out on one of the posts above, there is a possibility that the move could affect your site's rankings if the ip address is blacklisted and the ip that your using is being shared with someone who is spamming. In addition the move could affect your site if during the transition your site is down for more than a couple of daysdue to DNS issues. Then it will definitely affect your rankings.
You might want to check an old blog post from Matt Cutts himself with regards to "Moving to a New Host". It's a good read.