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Not that it helps, but you'll probably find that most ISP's will charge for a static IP. Those that don't and usually niche providers (like A&A) and will have higher monthly costs anyway.
Not specifically static but my IP on virgin hasn't changed in well over a year, plus the last octet is the same as my customer number on the hostname I don't think it will anymore either. Used to change every couple of days previously.
Register for an account on a dynamic dns site, (I use dysdns.org but think you have to pay for it now) then put the account and host name in the router. Doesn't vary too much really most routers are similar, the netgear ones are quite easy to use.