Work experience in graphic design, in fact any design discipline, is to my mind, vital. Do as much as you can throughout your entire education and make it as varied as you can.
Before I got into university I did two weeks work experience at Thorson's publishing in Wellingborough. This was a far cry from the swanky London agencies I did work experience at later in my 'career'. But it was still useful. My job was to cut the covers of books with the titles '60 ways to improve your caravan' and 'What star sign is your cat?'. I had to stick these covers onto boards (called show cards) in 'a creative way'. Basically in a fan shape. I did this for two weeks. I was pretty good at it in the end. I didn't learn a lot about graphic design, I was in a studio, where real graphic designers were at work. I got to master a scalpel and Spray Mount.
When I was at university I went and did work experience every single holiday. From a one man band to the huge creative behemoth; Imagination. Because of the sheer variety of my experience, I understood then where I wanted to be when I graduated.
So, if you are looking for work experience, keep your options open. Try a big agency and a small 'local' one. I say local, because London is not the be all and end all. I think everybody should try one London agency, if you can get a sofa to sleep on.
Getting work experience isn't as easy as you might think. Just because you will probably be working for free, or at best to cover your expenses, it doesn't mean the door will be wide open. Agencies get a lot of inquiries about work experience and some of the would be candidates are awful. It is likely you will have to apply, just in the same way you would if you were applying for a job. All that stuff (blatant plug warning) in 'What to put in your portfolio and get a job: Graphic Design' is still relevant.
Choose a few agencies, more than you think you'll need. Create a huge list. Call them and ask the receptionist or whoever answers the phone what is the best way to apply for work experience. You may get the brush off immediately. Don't take no for an answer. A receptionist's job is to say no so that busy directors don't have to take calls. If the answer is no, a well put together letter to the Creative Director or Studio Manager may still get you in.
If the agency does have a procedure for applying, follow it to the letter. Bear in mind, you may have to wait 6 months or longer for a space to be available. So plan well in advance. Start looking and asking in your first term. It does not matter if you feel you are not 'experienced enough'. No better way to change that, than work experience.
When you do get in, work your socks off. Never ever be late. Never sit there and do nothing. If you have nothing to do, ask if you can help. Make a cup of tea. Making tea might feel like a waste of time, but what better way to get to talk to everybody in the team? Most people like someone making them a brew and then you can talk to them about their work and maybe they will take the time to teach you a thing or two.
That is the real issue with work experience; everybody is usually so busy they don't have time to teach. Stick with it.
If you get on well and you have enjoyed yourself, they may ask you back. Now that is a result. When you come back, you will know the ropes. Chances are you have been useful and if you are useful, chances are you will get to work on real projects and learn from the team.
Most work experience is unpaid. Most agencies will offer to pay your travel and perhaps some expenses. Not many give you a wage. Some agencies, the rascals, will ask you to pay them. Don't do that.
You will note that I talk about work experience rather than internships. Work experience is usually shorter than an internship. Interns tend to be older and further along their education path. Internships are harder to come by, and can be paid. I'll talk bout them in another post.
Good luck.