Courtney
The biggest issue with the badges on the net is that they are Crown Copyright and MOD IRP have the licencing rights for them (and they will charge you for usage of them in some shape or form if you use them officially outside of service usage). Seems to some of those badges have the squadron number in Roman (CXI) and others in Arabic (111). Whatever is on the Sqn Standard and the badge signed by the Queen is the correct one (I suspect its the former, though the two high quality copies I have which were both produced by the Strike Command Graphics Office (one of them from the poster of operational RAF Squadrons in the late 70's / early 80's and the 2001 RAF image manual are different in that both formats of numbering are used (Roman on the 1970s one, Arabic on the later)).
(Addition after typing the above)
Big Unit Specialist is spot on reference Air Command Graphics holding the majority of the unit badges, thought as stated, the 111 Sqn badge they have may be incorrect in the number format used (The 6 Sqn badge that they produced on the two sources I listed above had major errors compared to what was on the original signed copy).