The mortgage on that will be using up around half of your income. That's insane.
£70k post-tax is around £48k so £4k/month so the mortgage will take around 30% of your take-home pay which is a fairly standard ratio.
Considering that looking at similar 3 bedrooms to those suggested for purchase gives rates of around £1350 / month. Even putting aside another 1/3 of your income (high) still leaves you looking at 5+ years to save a deposit.
60k/(48k*1/3) = 3.75 years
And that's assuming you start from zero savings.
However what mortgage lenders do is "stress test" at 5%-6.5% that means they evaluate if you'd be able to afford to pay the mortgage + cover your essential costs (food, energy, etc.) if rates rose to those levels.
It's essentially a worse-case assumption to ensure you wouldn't be bankrupt if that happened, not whether you'd be comfortably off at that level.
If interest rates were to rise in 5-10 years time don't forget you could also remortgage to a longer time period to significantly reduce monthly payments if you needed to.
Rates aren't going to jump overnight; if they rise it'll likely be a long slow-rise by which point you should have already paid down a meaningful percentage of your mortgage.
The median cost of a room in a flatshare in Zone 1/2 is just under £700 month, that's £8.4k/year. Let's assume other costs of living to be £10k/year that gives us a total of £18.4k/year.
Let's say you want to save £40k over 4 years, so 10k/year, that would require a take-home salary of £28.4k/year which implies a pre-tax salary of 37k.
37k should be comfortably achievable for a software developer 1-2 years out of uni.
And you still have to add the expenses on top. Food, transport, council taxes, utilities.
But if you rent in the suburbs you can get a similar discount on rental as you get on purchases.
(Although the 3-bed was just an example obviously you can get a 1-bed for a cheaper price as well)