If you labour with a first baby on gas and air, you will have a lot of pain. But saying that you want a c/s because of pain is not realistic, even if you could talk the doctors into doing it, which you wont!
Having an epidural will not increase the risk of a c/s, although it will increase the chances of an instrmental delivery because it reduces your ability to push, especially if given early.
Sometimes it speeds up labour, sometimes it stops labour - wish I could figure out why!
And it is usually effective and will work well, anaesthetists do them all day, every day, so not having one in case it doesnt work is not really a good option.
I think you need to look at all pain relief options, from TENS, gas and air, Diamorphine/Pethidine, epidural, to hypnobirthing and employing a doula, who would give you massive support in your choices.
Also, Royal Free has a very good birth centre, with excellent, supportive midwives and you might find this a better option. The main labour ward is just next door, as is theatre if you need it, so this might be worth a thought. You can call them for a tour.
Good luck.