If you didn't agree to pay for his legal costs when you agreed to buy the business subject to finance, then you are not obliged to pay them and he cannot refuse to sell you the business just because you don't agree to this additional item. If they insist you must agree to this for the sale to go through then if you want to get out of the deal just write to them and say "fine consider the deal off."
The broker's threat (that if you don't accept their terms and pay the deposit that it will somehow affect your reputation such that no one will deal with you) is rubbish. Business purchase deals fall through regularly over disputes about the terms of a proposed sale and in circumstances where they are tyring to impose an additonal term that you never agreed to, that is not an issue that would affect your ability to sell to other vendors. More likely the broker is just trying to pressure you to agree.
The fact the agreement was done through email to purchase the agreement does not of itself mean the deal is not binding, however, it appears in your case that either they are trying to insist on additional terms, or alternately you may have agreed to enter into the agreement contingent on agreeing some the terms but now cannot do so, either way it is most unlikely a court would consider you bound to proceed in such circumstances.
If you instruct your lawyer you want out, then provided they do not drop their insistence on this term that you pay his lawyers costs, then you should be able to withdraw from the contract without difficulty.
Good luck and PLEASE RATE MY ANSWER.