Every time anyone asks about this, up pop the sanctimonious people who would be perfectly happy to see their family assets built up by both parents handed over to someone who has only been part of their surviving parent's life for a short time and who then leaves the money to their own family. It is an absolutely normal and reasonable expectation that if your parents have any assets at the time of their death, once they are both gone, the money should pass to their children or grandchildren. This is what will happen when my Mum dies and it's what both she and my Dad wanted. This is what I want to happen when my husband and I are both dead. This is what the vast majority of people want.
Of course nobody has a right to inherit anything and many people won't because their parents never had any money or it all had to go on care costs. However, where there is money, if there is no will the intestacy laws say who gets the money, and, surprise surprise, children's interests are protected because Parliament recognises that most people want to provide for their children and grandchildren as well as their spouse.
In England and Wales the spouse or civil partner gets personal effects and the first £322k, which of course in many cases means they get everything. However, if there is more than that the amount above that is split - the children get half of it.
In Scotland Gov.uk says:
The husband, wife or civil partner gets the house up to a value of £473,000. They’ll get a lump sum of £473,000 if the house is worth more, and may have to sell off the property.
They also get:
furniture and moveable household goods up to the value of £29,000
up to £50,000 in cash
a third of the rest of the estate
The children will get two-thirds of the rest of the estate.
If a son or daughter has already died, their children (the grandchildren of the deceased) will inherit in their place.
This is what it says about Northern Ireland:
The husband, wife or civil partner keeps all the assets (including property), up to £250,000, and all the personal possessions, whatever their value.
The husband, wife or civil partner must survive the deceased by at least 28 days to inherit.
They also get one third of the rest of the estate.
The remaining two-thirds are shared between their children.
If a son or daughter has already died, their children (the grandchildren of the deceased) will inherit in their place.