University students are granted access automatically. Journalists just need to present their professional credentials ( and a utility bill for proof of residence ).
The rest of the commoners? Depends on the attitude of the assessor as to whether your topic of research is subjectively 'worthy'.
I've tried once, didn't gain approval and there is no appeals process.
What good is a ( tax-funded ) library if you can't use it?
In London again in 2014 I decided to check out the new British Library, heavily promoted. Surely things have changed. I rock up. There are any number of guides, promotions, pamphlets, exhibitions, whatever on offer. After a while though I realised that I wasn't going to be in luck this day either. I approached the friendly ladies at the information counter. "I just want to go into the library and read some books. That's not going to be possible is it?". "No, no it's not" she replied just slightly sheepishly.