To the OP, you can only offer what you've saved + what the mortgage company will loan you. But there are some chancers out there.
Bare in mind record low interest rates, with some commentators forecasting significant rises in interest. Citing that its needed to cool the market down, especially in the south (baffles me how any normal working person can afford housing in the superheated housing market down there).
As for 'it's now worth £ insert random number, more in a short period, that's all relative to where you live, everything else around about has also shot up by similar amounts. My sisters both have houses in Ealing, both were bought for a five figure sum, both are now property millionaires, but to move to similar properties, they'd need to hand over all that 'profit' for the new property. To move to a better area, they'd need to fork out more.
Anyway, all my sympathies lie with young people/couples trying to get a foot on the ladder, it's bloody hard.
Good luck to the OP