I have just switched from Vodafone to Pure for landline phone and broadband (was out of contract) and have experienced similar devious tactics.
Switch-over took place in early Feb but Vodafone continued to bill me for remainder of Feb and for Mar.
A long debate/argument (53 min call) ensued with a customer service rep who was adamant that my service was still "active" and that Pure did not take the line over properly (Pure have maintained that they did). A subsequent call back from a manager gave me the same story. They offered to cancel the service on the current date but not to reimburse me for days since the switch-over, claiming Pure should be paying for this.
The process to file a formal complaint with Vodafone is at [broken link removed]
I got a letter from Pure confirming the successful port-over date. I phoned up Vodafone again to get a "complaint reference number" (needed to file formal complaint online). The agent wanted to trace back again through the history - at this point, I said I just wanted the reference number to proceed with a complaint. Was forwarded to manager who said they had (surprisingly!) discovered a systems error and that my line had in fact been ported over correctly to Pure. They were now willing to cancel the Mar monthly fee.
I asked them to also reimburse me for remainder of Feb to remove double-billing and they cited a 30-day notice of cancellation that I was required to give (despite being out of contract). This doesn't sound right to me, so I pushed ahead with getting a complaint reference number and have filed a formal complaint with them online. Am tempted to cut my losses here, but want to press ahead out of principle as am curious to see what the outcome is...