The site looks great ..well done :)
Because you are using canvas this is quite easy.
Go to existing http://www.hppf.hcri.ac.uk/ website
1) Go to Tools/Export. Then Export all content to a file. Save file to PC.
2) Go to Canvas/Back up settings. Download Export file to PC.
Go to new WordPress website..
3) Upload and activate the Canvas theme.
4) Go to Tools / Import. Import all content from the file that you saved in Step 1 above.
5) Go to Canvas/Back up settings. Browse and upload the file you created in Step 2 above .
6) Re-select and click save your menu as the Primary menu. Found in Appearance/Menus.
That should be it. I have sometimes found that you need to upload your slider images again, but test first.
ps is that kilimanjaro ?