I’m fairly sure that the Royal Mail website just sells stamps at face value.
I have seen discounted stamps on a famous auction site, but if you do buy them there make sure they are genuinely unused and not merely “unfranked” which means they’ve been through the postal system before (and therefore shouldn’t be reused). If they’re described as unfranked, gum-free or for philatelic interest only, give them a swerve.
For a wider selection of discounted and valid postage I’ve used Philatelink in the past. They sell mint stamps that previously formed a part of people’s stamp collections. They’ve never been used and so remain valid, however, their stock on everything is low because of a combination of increased demand for postage and the drying up of their usual routes of supply such as stamp fairs.
With the new stamp rates I use two first class stamps (£1.70) plus an airmail sticker for any cards going to Europe, and I use two second class stamps plus 13p of make-up stamps (£1.45) for postcards going elsewhere.