I live in a country where about 90% of women have an epidural and other forms of pain relief aren't really available because they consider that the epidural is the only form of pain relief that actually works. Because of that, no woman has to fight for an epidural (it's actually more difficult to refuse one), and so she can pretty much guarantee that unless she's literally about to start pushing, if she asks for an epidural she will get one pronto.
I've never given birth in the UK but I've heard many stories of NHS midwives trying to discourage labouring women from having an epidural, telling her she doesn't need one and just needs to woman up a bit, telling her it's too early or too late, telling her it will increase the risk of complications (it won't).
In my opinion, if you think you would like an epidural you should talk to your midwife at an early stage, say you're very afraid of labour pain, and you want your birth plan to based on having an early epidural. You can always decide you don't want it, or don't want it yet, once you're in labour. If you get pushback, you could even start talking about having an elective C-section in that case, because you're really afraid of the labour pain. If they are ideologically opposed to epidurals they will probably also be ideologically opposed to elective C-sections on maternal request, and probably think the epidural is the lesser of two evils.
The point is, have a birth plan which is clearly centred around receiving effective pain relief when you request it (and not three hours later).
In my opinion you get the most benefit from an epidural when you have it once you're in active labour, and when you probably have enough hours of active labour ahead of you to fully benefit from the pain relief. Women who have bad experiences with epidurals are usually the ones who get them at a late stage, having suffered through hours of long and painful labour beforehand, and who are already scared and stressed and tired. Whereas women who get one nice and early before the contractions have become too painful quite often have nice stories of lying down for a nap, or watching box sets until it was time to push.