Well there are also companies like EZPZHosting which are quite reputable in .
Most hosting provider will require you to provide justification before a dedicated IP can be provisioned to you. If you do not use a SSL certificate, there will not be any purpose for a dedicated IP.
I know a few names of a very good web hosting providers in UK, but I'm not allowed to post recommendation and I might not because I never tested their service myself. So my suggestions is to check in the "Find a Host" section, to search the forums or to try to find more about UK web hosts that participated to HostingCon 2009... check exhibitor's list (hostingcon.com/exhibit/list/), the lists of registered attendees, the hostingcon's blog. If this is not enough, then you would search in the british local directories or to try any other resources.
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Ignore the UNLIMITED web space and bandwidth providers. Multiple domains can be easily hosted under Linux shared hosting account and you don't need to pay extra for it. I'd suggest you to go through the offers section.