Besides Redstone's fixed-line assets, Daisy will also pick up its mobile services and distribution unit Symphony.
Redstone's other units, convergence business Redstone Converged Solutions, infrastructure services and intelligent buildings specialist Redstone Managed Solutions, and its Irish storage business Redstone Technology are unaffected by the move.
Redstone was unavailable to comment.
In a statement, Daisy CEO Matthew Riley said the acquisition strengthened his position in the reseller market.
"This transaction is another step towards the group consolidating this fragmented sector and we will continue to pursue this strategy," he said.
Daisy Group was formed at the start of July after ISP Freedom4 - formerly Pipex - performed a reverse takeover of Yorkshire-based Daisy Communications, as well as web-hosting and network services provider Vialtus.
Earlier this month it swooped again on Eurotel and AT Communications, which had fallen into administration.
The firm has made no secret of its ambitions to build an independent comms powerhouse that could rival BT.
Its latest deal will complete towards the end of the month if everything goes according to plan.