Am thinking of doing the exact same thing to pump water from two butts on the annexe and workshop (will connect them together via gravity when we do the patio) to two interconnected ones at the end of the garden.
The issue will be detecting when the butts at the end are full, of course.
Hozelock do a (obviously chinky rebadge) Water Butt pump, the issue I think with 'storm' or flood submersible pumps I think is that they are not designed to maintain a sensible pressure - just as much pressure as possible into the biggest pipe possible?
The other chinky waterbutt speicifc pumps do look cack though.
Do you have level access to the tanks? If so then there is an alternative hozelock model that might be more suitable, especially as it works by switch, not float.
https://www.amazon.co.uk/Hozelock-7606-0000-Garden-Pump/dp/B078ZS6VLV/ref=sr_1_7?dchild=1&keywords=hozelock+pump&qid=1586856669&sr=8-7