Do you have to have towing mirrors by law?

For most tow cars and caravans yes.

Info here, as a diagram of what is required.

http://xtremeauto.co.uk/images/com_hikashop/upload/rv-3200b.jpg

It's the field of vision that is the legal requirement, not simply the using of extension mirrors. However, as Easy said, most outfits will need extension mirrors to achieve the legal requirement. 

Yes, trouble is if you clip a cyclist or similar you are onto a loser before you even start if no mirrors are fitted, regardless if it is a direct contributing factor or not.

Why would you not want to use towing mirrors? I used to tow with a 4x4 and I can't imagine towing without mirrors. 

David

 How big/small Is a '4×4'? An Audi Q7 is 4 wheel drive as were some  Fiat Pandas 

Easy T says it all!

The law requires you to be able to see down both sides of a trailer. In almost all circumstances if using a car to tow a caravan you will need extending mirrors. It is illegal to drive with them on when not towing though so do remember to take them off again.

Even  if  your  wide  towing  vehicle  gives  legal  views  down  the  sides/rear  of  your  narrow  caravan  you  can  still  expect  to  be  pulled  over  by  the  law  in  order  to  check  that  you  actually  are  legal.

It's  much  the  same  as  some  police  stop  motorcyclists  wearing  helmets  but  no  other  protective  clothing,  like  the  French  police  were  dressed  while  they  were  with  the  T de France,  rather  resembling  the  American  police   on "Chips"  the  T.V.  programme .

Surely you'd need to actually see a copper on the road to be pulled over. Other than when shutting a motorway for hours at a time, I very rarely see them out & about.

Come,  Come  It's  Sunday  --  I'm  always  nice  to  people  on  a  Sunday 

To  Be  Fair  I  understand  what  you  mean,  but  one  slip,  on  a  day  when  you  have  300  miles  towing  to  cover,  and  out  they'll  come  like  biting  midgies  when  you  have  short  sleeves  on  !!