The P-51K was basically just a D with a different propeller. The RAF called their aircraft Mustang Mk I, II, III and IV.
Early Mustangs with the single stage Allison engine had a number of different variants. The RAF called them Mustang Mk I, IA (the rare Hispano variant) or Mk II, the main differences being in armament layout. In US service they were P-51, P-51A or A-36, the last was a dive bomber variant with air brakes. A few of the RAF's Hispano Mustangs were used by the USAAF as camera equipped recon fighters, can't recall the designation offhand. The Packard Merlin equipped Mk III and IV were equivalents of the B/C and D/K.
The RAF's P-47s were all Ds and only varied from the US versions in minor equipment, radios and bomb racks etc. They replaced Hurricanes in the SEAC theater and were used for ground attack mostly. Can't think of a good source on SEAC Thunderbolts right now, but I'll let you know if I do.