Websites on subdomains

I am searching a web host and was told that I "have to" get a VPS for what I want to do and I wanted to double check with you if that is true (and not that I pay for a service that I don't need).

My plan:
1) Create Website 1 on Main Domain = http://www.example.com which is based on the Joomla CMS
2) Create Website 2 consisting of OpenAtrium (Drupal) on Sub-Domain = start.example.com
3) Create Website 3 consisting of Moodle (Open Source Learning Platform) on Sub-Domain 2 = learning.example.com

Do I really need a VPS or can I go just with shared hosting. Was thinking about squirrelhosting or lcn.

Could you recommend me a UK based cheap server for my purpose?

i don't see anything special in here.. you can do it fine without any problems on a shared host.. it lets you add subdomains, it has mysql databases, it has php.. just check if any of those programs have any specific requirements that might not be available on the shared host..