I have one of these, or one very like it:
https://www.ebay.co.uk/itm/Brand-Ne...-Unlocked-Mobile-Phone-WARRANTY-/283000161062
Got mine for a tenner or not much more when they were still just about current. Unlocked.
Great phone - nice keyboard, which can (oo) be set to light up. Nicely made, nice feel, dropped it a fair few times with no great problems. Great for calls and texting. Nicely made. Small. Battery lasts for ages. Spare batteries can be obtained for not a lot from
ebay for probably evermore. No frills, not even a radio or camera. Oh, makes a great alarm clock. Unlike some smart phones you can switch it off at night and it will, clever smart thing that it is, wake itself up to sound the alarm. Other basic functions like a countdown timer with alarm - handy - I set it whenever I out the espresso pot on the stove so that I don't forget it and fry the pot.
Worried that all remaining stocks would be buried in a purge I bought another second hand pretty much as new off ebay for a tenner.
Note that it cannot be used on the Three network. As it's 2G.
Mine is on Asda mobile - nice and simple.
Be aware that there is another basic phone under various brandings (forget them) that is appalling - sound quality dire and it, believe it or not, doesn't have predictive tesxting.
PS - can't help but be intrigued by your "privacy reasons".