The RAF used the Mustang III and IV in ETO and MTO for recon, escort, fighter bomber CAS in both theatres.
At first the RAF preferred not to modify their P-51B-1 and P-51B-5/C-1 with 85 gallon tanks but most were loaned back in late December, 1943 to 9th AF 354FG and 363FG and 357FG at request of Doolittle/Spaatz. Many were modified for the 85 gallon fuselage tank to perform 8th AF Long Range mission. Many were returned in that condition and virtually all the new P-51B-10/C-5 that incorporated the 85 gallon tank at the factory were left in but mostly not used except for long range escort,
The RAF supported 8th AF on several March/April 1944 missions in addition to escorting their own B-25s, etc in daylight. Later, when Harris was coerced to join the daylight campaign against Oli, the RAF preferred RAF Mustangs under their control for tactics - they did not approve of the 8th AF Fighter Group "See the enemy - attack the enemy" but could control their own Mustang squadrons to perform close escort. In the MTO, the roles were similar but I don't recall reading of RAF Mustangs escorting 12th AF medium and light bomber attacks.