Thanks for the advice. I first tried calling Digiweb accounts just to ensure my DSL line was definitely with them, but the person told me that I must contact their sales. Their team seems to be quite small, as I ended up with the same person again when I rang back with the sales number they gave me, followed by a voicemail system on the 3rd try later.
I called BT straight away afterwards. I see that their queue buster system is back up again, as after about a minute of being on hold, it gave an option to ring my phone or another number when I reach the top of the queue. I really wish this is something Eircom would implement, as their 1901 support waiting times are terrible. This is the main reason I'm staying clear of Eircom broadband.
Once I got the call-back from BT, I explained the issue to BT and according to them, they were never informed about my change of DSL provider and as far as they could see, I still had my DSL line with them. They cancelled my service and refunded me as far back as June. Just a pity I tested my old IOL BT DSL router sometime in June, as they would only refund as far back as my last logon to their DSL network, but at least it includes this €80 charge.
I later got a call back from Digiweb confirming that they are in control of my line and have proof from Eircom confirming this.