Speed up backend?

Hiya, One of my sites is glacially slow at redrawing even the simplest page.

I understand if there are loads of large images it will take a long time to load, but even a new page with NOTHING on it takes a good 10 seconds to load

I seem to repeatedly get this error too:
Connection lost. Saving has been disabled until you are reconnected. This post is being backed up in your browser, just in case.

Despite all other websites work as normal.

I have a 350 MB fibre broadband so this isn’t the problem. I have asked the hosting company (Fasthosts) and they say the problem is the number of large images, but this still doesn’t explain the “Connection lost” error.

It get the feeling the problem is more to do with accessing the server. The same server is used for other websites which don’t have this problem.

Is there a way to give the domain a lobotomy and speed up the backend?