I've watched a few of these programmes and wondered too about how they often suffer a loss on a car (not even taking into account what they may have spent on parts and time). However, at least a couple of ideas come to mind:-
1, They are probably getting a good few quid off the production company making the program (it's good business for the production company as it's fairly cheap/easy TV with a reasonable market for distributing around the world as everybody likes cars). So, they are possibly making a net profit? Would they keep doing if they weren't?
2. Sometimes you see cars not selling at auction because they don't meet a high reserve. However, after the auction what's to stop one of the bidders doing a private off-screen deal with the seller? Consider the
purely hypothetical scenario where a car is being auctioned with a reserve of $200,000. If someone bids this. They shall have to pay $200,000 plus the auction's commission (say this is 10%). So, the buyer has to cough up $220,000. As the sale has all been above board it will also have to go through the buyer's/seller's/auction's business accounts too. So, no hiding the fact from Mr Tax Man that $220,000 has just changed hands. Well, let's say the car doesn't reach the $200,000 reserve at auction. However, a few weeks later, one of the bidders, buys the car from the seller for $200,000 - he has just saved himself a whole lot of money ($20,000), the seller gets what he was looking for and that's before you even start to look at any creative accounting that might take place for tax purposes (e.g. buyer paying with suitcase full of $200,000 cash and seller putting the sale through his books as $100,000). Gosh, darn it, made a loss again!