As long as you and baby are healthy they will tend to send you home as soon as possible after giving birth. This is due to their belief that you'll recoup better in the comfort of your own home rather than in a hospital. Also, for the first 10-days after baby is born (whether a home birth or a hospital birth) you're still under the care of your community midwife, who will come to your home to check to see how you're doing and coping. After you've been discharged by the community midwife, you'll get a home visit from your community health visitor, who is a nurse that you can turn to for general help and support from birth to 5yrs. So, just because you've left hospital, doesn't mean you don't have a medical support network.
Birth-wise, here in the UK you're in charge of your notes and your birth plan. Obviously, depending on your past medical history and how your past births went that can affect the way your birth is monitored and guided here, but generally, as long as you're not putting yourself or your baby at risk, you have the ultimate say (not your partner etc.) in the delivery room as to how you want your birth to go.
As mentioned by others, I think the natural methods of pain relief are pushed before drugs, but ultimately the decision is yours (unless timing or for monitoring reasons the drugs would not be beneficial).
As for what pain relief is available, you'll need to familiarise yourself with the individual hospital you're looking to give birth at and what their policies are on epidurals etc. if that's part of your birth plan. My hospital, where I had both of my children at, had a policy with epidurals that they would only be electively offered during "normal business hours" (Mon-Fri 9am-5pm), but out of hours or weekends they were for emergencies only, though they were looking to possibly change that. But, that was something my Midwives and OBGYN let me know about in advance. Personally, I had Entinox, TENs and Diamorphine for my first birth and TENs and Entinox only for my second. Both of my children had to be induced as they were overdue. My first birth was 13 hours from start to finish and my second was just under 4 hours.
Again, for Maternity and birthing wards, that varies from hospital to hospital. I had each of my children in private birthing rooms, which was standard for every Mum at my hospital, but within hours of giving birth I was moved onto the post-delivery Maternity ward. With each of my children I was kept overnight for observation because of slight complications during birth (an unexplained excessive bleed with my first and my son pooed during birth with my second), but always felt that I had support of the midwives on duty. Generally, here in the UK babies are kept at their mother's bedside. This way you can feed your baby and bond with them if you do end up staying in hospital. You'll find your baby will be tagged on their feet and wrists, and that all staff coming to check baby should check all tags and yours to make sure that there's no mix ups.
If you want your own private room post-birth you'll have to check with the hospital you're looking to give birth at, as to their policies. And, be prepared for the eventuality that you possibly may end up on ward anyway, as they usually only have a limited amount of private rooms, which will be paid for on a first-come, first-serve basis.
When you are discharged from the hospital, you'll usually already have a visit lined up and be made aware of who your community midwife is and how to contact them if you need to speak to someone about any concerns you may have. Comminity Midwife visits happen 7-days a week, so their care is usually quite thorough in trying to look after both Mum and baby.
If you have any more questions just ask.
PS - have you seen the show
One Born Every Minute http://www.youtube.com/user/4oDDocumentaries?