I just cancel my DD online when the last payment of the annual policy has been taken out, that usually prompts some kind of response.
On another note the thieving bastards at the DVLA ripped me off for Road Tax. I sold a van to my mate, we settled on the 1st July, I did the vehicle transfer online. As it was a monthly DD my payment was taken on the 1st, my mate also paid from the 1st July, no problem I thought, I'll get a refund. It said on the website it can take 6 weeks to come through. Forward 7 weeks later the refund of £29 has not come through, I rang them, they told me I'd not transferred to vehicle until around 8am in the morning and therefore I was liable for a month's tax as I owned the van for 8 hours during July. I told them my mate had taken ownership from midnight of that date and insured the vehicle accordingly, that didn't matter one bit to the twat at DVLA.
If anyone gets involved in selling under the same circumstances just Sorn the vehicle before midnight on the last day of the month and ensure the new owner taxes it from the first day of the following month.