Private pilot licences come in (at least) two types.
VFR and IFR.
VFR stands for visual flight rules. This is the most basic type of pilot's licence. It means you are only allowed to fly in what is basically good weather.
You have to sit I think five theory exams for the VFR PPL (visual flight rules private pilot's license). One of which is weather and how to predict it and where to get information about it.
IFR stands for instrument flight rules. This does NOT mean you can fly in any weather (some weather is just flat out dangerous to fly in) but it means that you can fly in cloud cover etc. in order to get an IFR PPL you need to learn how to fly on instruments alone. So usually the instructor will make you wear what are called "foggles" which are goggles that let you see the instruments but obscure the sky.
When you are going to fly, you should plan your flight first. This means checking the weather properly (ie not the bbc). There are sites you can subscribe to which will give you a detailed weather prediction for all airports in the U.K. hour by hour.
If you are flying under VFR it is your responsibility to check that visual flight conditions obtain for the whole flight and the club you are renting the plane from will expect this to be included on your (paper) flight plan which you need to file with them before you take off. They usually have someone there who checks it before you go well - I've been up with ExH when they've warned about rain showers coming in etc.
Everyone should file a flight plan under all circumstances. Even if you own your own plane it's standard to file one with the departing and arriving airport.
Your plane if you are renting from a club will have a transponder which squawks a number. In most areas of the UK (because it is very populated) air traffic is watched by radar of some kind or other.
So for example say I was going from Cambridge to Norwich. I'd be in contact by radio with radar/air traffic almost continuously.
Before I left I'd have to ring Norwich to check they are ok with me coming. (Most airports in the U.K. are prior permission required ie ring us and we'll tell you if we are open/you can have a slot). I can only go if they are ok with me coming.
So. Air traffic at Cambridge give me instructions to depart. I take off and stay I touch by radio. I can hear other planes on the radio and what air traffic tells them gives me pretty good clues about where they are.
Then I switch to Cambridge approach (different radio channel). I request radar service and tell them I'mgoing to Norwich. They tell me to sqwak 3345.
This means that on their radar screen they see me as the number 3345. I've requested radar so they'll tell me if any other aircraft is anywhere near me.
From Cambridge Approach I switch to Lakenheath (American military but still provide radar service for small planes) and so on until I get up to Norwich.
At pretty much all points I'm on someone's radar screen and they're keeping a general eye out.
Obviously I am looking out as well😀