Replacent gas boiler room thermostat

bob_a_builder

Going down the DIY & keeping it simple route .....  - but if you are not DIY competent / confident - DON'T Touch 

A simple 7 day battery powered thermostat can replace that stat and will do 98% of what you need.
OK you won't be able to change it from your armchair, but once the 7 day program is set to match your life style you probably won't need to change much on a daily/weekly/monthly basis 

Something like this 
https://www.tlc-direct.co.uk/Products/SMTRT035N.html

It would give you this level of control ...
6 different periods thru the day which could be different temps and that could be the same or different for each day
manual here
https://www.tlc-direct.co.uk/Products/SMTRT035N.html

These thermostats will have a set of relay contacts  marked NO , NC ,  C     - you just need to wire the C and NO  to the existing switch contacts of the existing stat
any other wires should be safely terminated

Let it control the boiler by setting the existing boiler programmer to CH always on 

I know you said you don't want a phone app, but just to say that a NEST E  would provide that with the very same wiring changes 
https://www.toolstation.com/google-nest-thermostat-e/p12651

away-with-the-fairies

Deffo not DIY.i can't even hammer a nail straight. I was looking at a specific worcester bosch one this morning at screwfix for £162. Haven't looked at others yet