Does Taverna require an OMII grid to be installed?

No. You don't have to install any other OMII-UK software to use Taverna. It is a stand-alone piece of software.

However, if you do need to access secure OMII services then you will need to install the OMII client along with your Taverna installation.

Note that newer releases of the OMII client includes a tailored version of Taverna. Although this might not correspond with the newest Taverna version, it is the one supported by OMII.