It's highly unlikely the UK will be attacked with nuclear weapons whilst a) we have a nuclear deterrent that we are willing to use, and b) only known states have nuclear weapons.
The concept of "MAD" (Mutually-Assured Destruction) means an attack on the UK will result in a nuclear retaliation against the state which attacks us. This can only be undermined if we have a PM who declares that (s)he would not use nuclear weapons to respond to an attack - such as Corbyn - or non-state entities get hold of nuclear weaponry. On the last point, by this the main concern would be Islamic terrorists, because which country should we target? It's one thing bombing Iraq or Afghanistan with conventional weapons, it would be a lot harder to justify wiping them off the face of the earth.
Of countries which have nuclear weapons, none are a serious threat to the UK at the moment. Israel, North Korea and Russia are perhaps the most unstable, but I can't see Israel wanting to attack us, Russia know that any attack by them will result in a MASSIVE response by the US, and North Korea are not currently much of a threat to anyone outside of their peninsular or Japan. If North Korea can develop submarine-based nuclear weapons then they would indeed be a serious threat to us. We don't need to worry about missiles fired from North Korea because they don't have the range to reach us - their main aim is to be able to reach the west coast of the US, which is a lot closer to them than the UK is.
If you are still concerned about a nuclear attack, then you can take steps to help yourself. Prepare for an attack by stockpiling food, water, fuel and medication. Have a plan as to where you will go - do you have a garden where you can build a fallout shelter, and if not then pick a room in your home with the least exposure to the outside (a hallway perhaps).
If you are near "ground zero" when the attack comes there will be nothing you can do - you will be vapourised before you know what is happening! If you are further away, you need to know what to do - immediately take shelter when you see the flash of the bomb (literally anything is better than nothing - a tree, a car, anything at all), then get home ASAP before fallout becomes the major concern. Then it's just a case of waiting it out in the shelter you have prepared.
But in all honesty, you don't need to worry about a nuclear attack. You are much more likely to die from a terrorist attack, at the hands of a serial killer-rapist, indeed to be murdered by your partner or own child.