I thought I'd give a long-overdue update to this thread for the benefit of anyone else experiencing this problem.
I found an excellent BT broadband engineer who discovered that the problem was caused by some telephone extension wiring being in very close proximity to the television's wiring. He solved it by disconnecting the bell wire and installing an ADSL-filtered faceplate, to which the router's modem was then connected.
I was also experiencing another problem whereby my Internet connection was often interrupted when the telephone rang. The engineer discovered that this was caused by a fault at my telephone exchange after completely disconnecting the house's wiring from the master socket. Our ISP, Demon, were horrendously uncooperative in resolving the problem, despite their legal obligation to ensure their equipment is in working order. The problem immediately disappeared after I switched to Be (who also use ADSL2+).