Hi and Welcome!
I guess, not.
With a normal (retail or system builder) Vista install disc, you could do that since the features (Premium, Basic, Ultimate) are determined by the product key during installation. The Dell OEM disc might install Home Premium without asking. If you can enter your home basic key after installation, then all is okay.
Apart from ordering a new set of discs from Dell, you may have a look into your manual if there is a recovery partition which will restore the factory preinstallation.
@pipemanid: Most laptops and brand name computers come without any Windows install disc, so the one disc - one license claim is IMHO not justified.