It looks to be from the 44-6xxx or 44-8xxx serial blocks.
Sadly the 306BG records are a little sketchy when it comes to assigned individual aircraft letters, and as they removed the squadron code letters from the fuselages and replaced when with different colours at the top of the fin a black and white photo makes things even trickier...

However, three 306BG aircraft within those serial ranges do have their individual letters noted as K: 44-6585, 44-8148 and 44-8197.
I'll keep digging to see if any of those was diverted to RAF Blakehill Farm at any time.
From the photo the serial looks to be 44-8x9x, so 44-8197 "Punchy" of the 376BS would be a good fit. She was assigned to the 306th on the 15th September 1944, so was certainly was in the UK at the right time.

All the best,
PB