The website has now been moved to HostGator. So far, so good. HostGator have been helpful when contacted and everything seems to be set up correctly.
The building work at the back of the house is progressing slowly due to the wet unpredictable summer we're having. We have some brickwork down today and hopefully the concrete floor will be in tomorrow.
I'll post some more next week about my experiences with EasySpace and HostGator.