Yes, Royal Mail tends to be far more expensive than USPS for letters and smaller parcels, including internationally (e.g. UK to US costs far more than US to UK), but they have relatively reasonable pricing on medium-sized parcels in my experience.
It definitely is apparent which is the private company based on their pricing schemes, even besides the more consumer-facing UK Post Office locations that are almost entirely franchised and often operate as a small convenience store, etc.
The prices have been increasing above inflation for years, but especially in the last few years - e.g. in 2001 a first class stamp cost 0.27 GBP (0.49 in 2024), and even in 2019 in was 0.70 GBP (0.86 in 2024).
It definitely is apparent which is the private company based on their pricing schemes, even besides the more consumer-facing UK Post Office locations that are almost entirely franchised and often operate as a small convenience store, etc.