House prices are mostly determined by how much leverage people can get to buy them. Look for example at unmortgageable houses (eg. due to construction type or land covenant), and they are around 5x cheaper for a similar living space.
House prices must continue to rise, or the debt-tower collapses, and everyone ends up penniless. Some people say thats what they want, but a real uncontrolled housing collapse would be far worse than 2008, and would likely end in a multi-generational economic downturn.
Successive governments have taken lots of moves to maintain high prices - "help to buy" ISA's, shared ownership, small downpayment mortgages, 'affordable' housing, etc.
Those things are also very politically convenient because to the layperson they seem like ways to make housing more affordable, when in fact the market result is house prices rise further.
Will there ever be an end to the rises? Maybe not... Inflation in the British Pound has gone on for hundreds of years. House price inflation can do the same. Will they continue to rise faster than inflation? Maybe... If you can construct more and more elaborate ways to get higher leverage. There are lots of options left, like for example the government could back mortgages with interest rates below market rate.