To find out where you can land and what is required before you show up, look up the relevant airfield in the AIP. A simple way of doing this is to use Pooleys or some other flight guide, which is what most of us do. However, since these guides tend to be out of date almost before they're published, it's sensible to phone the airfield anyway and check. That phone call should also ascertain if they're closed for some reason, eg a sudden accident and a blocked runway. However, if an airfield doesn't say in the flight guides that they're PPR, it's quite OK to just turn up if you want to.
GA aircraft can land at almost any airfield in the UK. I think Heathrow is the sole exception, but I'm not certain of that. A year or so ago I landed at Manchester - phone in advance to get a slot, no problem when I had to change it due to an electrical problem, no problem again when I was a bit late for my slot, very helpful if you get lost on their forest of taxiways, and only £35 landing fee (technically departure fee or some similar name).
Licensing of airfields has nothing to do with whether you can land there or not, generally. Training flights need licensed airfields; I don't know if anyone else does. Various small airfields are unlicensed after, say, 5pm, as they have no fire cover, but they may be quite happy for aircraft to take-off and land outside of those times...but you need to check. I remember a sunny day at Sleap one summer, and it was unlicensed but crowded after 5pm. Some well-known and frequently used airfields are not licensed, Popham being the best known example - which is why there is no ab initio training there. And most microlight fields are unlicensed, but you can often still land there with permission and if your aircraft and skill level can cope with the short runways.
If in doubt, phone the airfield and ask. I usually phone everywhere now, and just say I want to fly in, and is that OK and what's the weather like and is there anything I need to know....forget requesting PPR and all the fancy terminology; just speak English, as one person to another. Unless it's a weather diversion or similar of course, in which case tell them that on the radio, and people are usually amazingly helpful.