I'm surprised that nobody has yet mentioned that
(a) all local florists are currently closed (other than as below) ; and
(b) nearly all delivery services, such as Interflora, use those same local florists to supply and deliver their flowers.
So you're going to find it very hard to get anyone to provide the service that you're seeking.
However a
few florists are continuing to accept orders placed through Interflora (et al) but that will depend upon their individual trading models. For example a florist's shop that normally takes lots of orders through Interflora every day might find it worthwhile to continue to handle such orders at the present time, whereas a shop that only gets business in such a way once a week almost certainly won't bother to continue accepting orders.
Those florists shops which are accepting orders through Interflora at the moment are only doing so on the basis that they're given free choice as to what to include in the delivery:
https://www.interflora.co.uk/content/florists-choice/
(i.e. you can't insist upon any particular type of flowers being included).
Further, as only a minority of florists are providing the service, you might find that there's no coverage in the area you require. (I've just entered my own postcode, here in Suffolk, and there are no deliveries available in my small town. Further, I've just tried a postcode for the county town of Ipswich and, again there are no deliveries in that area. However a Sheffield postcode does come up trumps).
So you could find yourself struggling to find a company to meet your needs. Sorry!