Large law firms generally don't use references as part of the recruitment process. I believe they are checked by the external company responsible for checking the truth of your application form after you have been offered a TC, this was certainly the case for me.
This is fairly standard in the professional services industry. No law firm or other professional services firm give meaningful references about the candidate. They will generally only confirm your title and dates of employment, no matter how good or bad an employee you were.
People can give negative references, but they generally don't. Law firms have the policy of only confirming title/dates of employment because they are worried about getting sued; it is quite difficult for a large organisation to ensure that all its references are accurate.