ValueVPS is a UK-based VPS company that has some cheap Xen or OpenVZ VPS plans that starts from £4.99/month. As of now £4.99 is still more than our threshold here which is USD$7.00, but ValueVPS also offers prepaid discount —

• £14.22 paid quarterly (~USD$6.95/month)
• £26.95 paid semi-annually (~USD$6.58/month)
• £50.90 paid annually (~USD$6.22/month)

And you get

• 128MB memory + 256MB swap or burstable memory
• 10GB storage
• 150GB/month data transfer
• 2 IP addresses
• HyperVM

Servers are in UK. Domain has been registered in September 2008 so only 3 months in operation.