Though by the sounds of it not as severe an issue as yours, was getting around 3 or 4 a day ....
I got a BT8600 call blocker phone which uses True Call and have not had a single unwanted call since.
Input your 'VIP' callers (those numbers you'd store on your phone anyway) these callers ring straight through. Any others are greeted by a recorded message asking them to announce themselves , if they do nothing, the call is instantly blocked, (the handset hasn't rung your end yet BTW) then the phone rings and announces whose calling, you can answer, block or tell to leave a message.
Other settings include being able to block all international calls, or withheld numbers.
It is also a 'nice' handset, easy to use, good answerphone. Money very well spent in my book.