Saving for a deposit on a single income — is it even possible?

I earn £34k in Nottingham. After rent (£650), bills, food, and transport I save about £400/month. At this rate it'll take me over 6 years to save a 10% deposit on an average property here (~£200k).

And that's assuming prices don't go up further. Meanwhile rent keeps eating into my savings potential.

I don't have family who can help with a deposit. No inheritance coming. Just me and my salary.

Is homeownership on a single average income actually achievable anymore or am I chasing a dream?