Where's scrimnet when you need him?
Fortunately his book has a section headed 'Badges that can be confused with Royal Engineers'. From that section I think the nearest alternatives would be the 18th Hussars or at a stretch, the Queen's Own Dorset Yeomanry. If we include the infantry, on the basis he might have been in the battalion transport section, maybe the 8th Batttalion Hampshire Regiment, the Isle of Wight Rifles. However on balance I think Jim1 and Shaun are correct and he's Royal Engineers.
Had a few log in issues!
Anyway...
Best way forward is...
1.ALWAYS scan the original photo at 600dpi
2. The shoulder title should show op under a scan. Is it two or three letters or more??
3. If you have no scanner try your local library who will be more than pleased to help.
We have a Parish internet cafe in the parish rooms in the village.