Okay pal, don't take this the wrong way but the answer is almost 100% a YES. The only thing that may save you is some insane determination, networking and strong family contacts.
Why do I say this? Well first off I'm assuming you mean a City law firm or something of a similar level.
There are loads. Hundreds. Far too many law students. Plus all the history->law and other courses->law conversions you see around, yet how many actual lawyers does a law firm really need? No where near as many as there are students. Whilst I have no first hand, solid information about law recruiting, I am at one of the 'top banking unis', that is the few unis that banks actively recruit FO roles at (So Ox,Cam,LSE,Warwick,ICL,UCL, then possibly Durham/Andrews/Bath if you're pushing it). Thus I would say that I am with some of the students who are most likely to become lawyers in the country, yet I know MANY who struggle for work experience and I cannot think of anyone who didn't get law experience through family contacts.
TLDR; there are SO many students fighting for SO FEW jobs that even the top unis with students who have contacts struggle to get lawyers in!
But it's not all doom and gloom. What can you do to maximise your chances?
Go to the highest rate uni you can, endeavour to do so because it will help you l o a d s and #15 >> #30... #30 wouldn't get a look into by a top law firm.
Network like crazy. crazy. With law students, lawyers, whatever. Build a strong network through uni, friends and family friends.
Get involved on campus eg be president of the law society or start a new law soc if there isn't one!
Get law / managerial / some really substantial work experience.
Good luck!
//also, it's affect, not effect.