I have heard it is possible to exchange houses with someone overseas for a holiday - maybe for some months.
Does anyone know of an organisation through which this can be organised
Or maybe a website to look at?

There are many. If you type in Home Exchanges on the Google website I am sure you will pull a lot up. Or probably if you type the same thing in on Fodor's you will get lots of info also

The phrase to search on, here or on Google, is home exchange. My favorite is homelink.

Home exchange #28 will be Rome, Italy for Xmas.

Home exchange #29 will be 9 days in Seattle at the end of March.

Home exchange #30 will be next August but no idea where yet.

I belong to both Homelink and Intervac. Their first set of books just closed out for the next home exchange year. Most deals for next summer are cut by the end of January. If you are interested, sign up for the second round of books. Most people do not get the books anymore and do their deals off the websites, so being in the first books is no longer the big deal it once was.

Also Digsville.com is an excellent site.
Cheers,
Jan