All of this really depends on the assumptions used.
Yes, 95% LTV mortgages do exist. But they are neither typical (average FTB deposit is about 15%), nor desirable - if you're getting a much bigger mortgage with a 95% deal, you get clobbered with much higher monthly payments (esp in a higher interest rate environment as it raises the loan principle to a much larger degree, so costs you exponentially more over the lifecycle of the mortgage), which can make them unaffordable to many. It's really a pick your poison decision, have the pain of slowly building a deposit while renting at extortionate prices or have the pain of much higher monthly payments. Evidence shows that most go for the first option, so while it's certainly possible to get 95% LTV deals, few do because they're fairly undesirable for many reasons. And none of this points to it being "not that hard to buy a home", it suggests that it's possible but very difficult.
On your pay point, I wish average earnings were 35k per year, the UK would be a much more prosperous country. Unfortunately, you only get to the 35k figure by making some generous assumptions. The 35k figure is if you only count full-time workers, and you exclude all self-employed workers (who on average earn a fair bit lower than employees), so the 35k number has an upward bias on two counts. Now, one could argue that if your goal is to buy a home then maybe you shouldn't be part-time and/or self-employed as it lowers average earnings, but there's little point discussing motivations, the reality is that people work in lots of different ways for lots of different reasons and only focusing on the highest paid group (full-time employees) and characterising that as the average UK salary is misleading.
When you look at the average over all employees (weighted avg of FT and PT) in the latest ONS ASHE survey, you get a figure under 30k, though this still excludes the self-employed. The latest ONS RTI estimate of median employee pay, which is much more timely than ASHE and uses actual PAYE data, puts it at under 28k - and this is still excluding the lower earning self-employed. A bigger issue is that you're using UK-wide earning measures, which get a very hefty bump from London and SE England pay, then are using that to judge non-London & SE housing affordability. If you were to look at average pay (excluding London & SE), it would be a fair bit lower than the aforementioned figures which paints a fairly depressing image I know. In reality, you're probably looking at 25k as average salary and given about 20% work PT, this averages to 1.6 FT salaries between a couple, using your maths this would net to about 160k and on a 95% LTV mortgage, the deposit barely boosts this at all. And if you want to add another layer of complication, average salaries generally covers those aged 16-64, but the age where you might buy a home is normally in the 25-35 period, where average salaries are even lower.
This all isn't to say that it's not possible to buy a home, just that I think affordability-wise it is genuinely quite difficult to buy a home, so for someone who's responsible for giving out the mortgages to say it's not that difficult, feels a bit out of touch. In reality, it's likely an excuse for NatWest not lowering the rates on their mortgage products as quick as rivals haha.