I don't think it should be free, but I think it should be cheaper.
Isn't a bit like condoms anyway, as far as products go? You CAN get them for free of charge at a sexual health clinic, but most people I know tend to buy them in the supermarket or shops or whatnot.
So in fact you have the choice whether or not to pay for it.
We are so, so lucky to have free of charge contraception in this country. And frankly, there are so many options that there is no excuse. Don't like the pill? Injection. Don't want the injection? Implant. Don't want hormones? The coil or IUD or whatever.
They aren't going to protect your sexual health, but these days there is absolutely NO excuse to have sex with no form of contraception behind.
If you are old enough to have sex, aren't a nun, and accept there is a possibility you might have a one night stand at some point, then you should be on contraception.