Will not having a graduates degree damage future promotion as an officer?

Hi there,
In answer to your question the simple answer is no. The entry requirements to become an Infantry officer is 72 UCAS points and 35 ALIS points at GCSE (including at least grade C/4 in English, Maths and Science or foreign language).
You begin with Officer training at the Royal Military Academy Sandhurst, which lasts for 44 weeks. You learn what’s expected of a British Army Officer and how to lead soldiers on and off the battlefield. If you join an Infantry regiment you go on to do the 16-week Platoon Commanders Battle Course in Brecon, Wales. After this, you'll be a capable tactician, as well as physically and mentally robust.
Once you have completed all elements of training and have joined your Regiment and in order for promotion you will need to complete the relevant career and education courses - for more information on becoming at Infantry officer check out this link - https://apply.army.mod.uk/roles/infantry/infantry-officer.