Sadly it's never going to become affordable for the following reasons;
1. Massive migration to the UK. I remember Tony Blair loosening the immigration rules for everyone which resulted in a net excess of 2.9 million coming to our shores. Thereafter we had the same government give freedom of movement to nations which just joined the EU back in 2005, which ran against expert advice. We now have 5 million EU workers and their families in the UK. With such a surge, the corresponding knock on affect on rent, house prices was astronomical.
2. Failure of successive governments to build more houses. Be it Labour or Conservative they are just not interested. Old council housing stock was sold off to people who cashed in and upgraded, but never replaced. When we do have housing developments, 90% of the new builds are put up for sale at market prices which price out the vast majority of first time buyers. Social stock also makes up a tiny fraction of the new development, as everyone knows its bad for business. No one will buy next to social housing.
3. The cash cow that is the landlord/property developer. Landlords and developers by the nature of the industry they are in tend to buy more houses. This results in good levels of stamp duty. With landlords they can also receive steady steams of taxable income. Yes they have made it harder, but not by much. I know of landlords e.g. several British Pakistanis who have several hundred properties each (yes you read that right). Such people are just going from strength to strength. It's actually the single home owner who wanted another property for investment that was hit, or the one who already has one and maybe wants to expand to make two.
4. Schemes that inflate demand. Like many posters have already written, the government just seems hellbent on scheme that hike up demand e.g. help to buy. 5% deposits are not hard to put together for a couple, this feeds into pricing strategies for developers, and for those who wish to sell their homes. The demand will just keep on soaring.
5. Bricks and mortar, the safe investment. There simply isn't any investment which has such a minimised risk and yet delivers good returns. As someone stated you don't even need to make rental profit i.e. just be able to cover our repayments and bank on an appreciating asset. So therefore anyone with significant spare cash will turn to property. Savings and bonds rates are low, the markets are deemed risky, so the choice is obvious .