If it's in the UK then once you do a training contract with them the larger law firms will pay for your fees both LPC and sometimes university fees. But what you need to do is prove that you are worth investing in and also sometimes you must continue with the firm for a designated period, even after the training contract, if offered the opportunity, otherwise you may have to pay the firm back for paying your fees.
You would have to already be employed by them. The larger law firms would NEVER commit to hire a law school graduate before they ever started law school, unless the person was currently working for them as a paralegal and they knew the value of that individual. Even so, I've known a number of people who had been working as paralegals for large firms, who continued to work for those firms during law school, and who got hired by those firms as attorneys afterward, and even they didn't get their tuition paid for by the firm. It must be an unusual situation for them to do that.