Mortgage market liberalisation saw lending increase from 20% of GDP to 80% by 2006, the vast majority of which went in to the purchase of existing homes. There is no feasible increase in supply that could have absorbed such a flood of credit.
The introduction of Buy-to-Let mortgages in the late 1990s, following earlier liberalisation of the PRS, ramped up investment demand further. Banks will always prefer low-risk borrowers so those who already have collataral (existing homes) will outcompete first timer buyers.
This is worth a read too, if anyone's interested in the demand-side drivers of housing inflation:
https://x.com/jryancollins/status/1844700553596559617
Report here:
https://www.ucl.ac.uk/bartlett/public-purpose/sites/bartlett_public_purpose/files/241009_iipp_policy_report_ukhousing_layout2.pdf