C16, many thanks for identifying 516 as a member of 18 Sqn. As you say, the Pegasus rampant doesn't reflect the standard design normally used by the squadron and (as depicted below) appears to have more in common with the logo of the oil company.
Perhaps 18's CO had an understanding with the MD of Mobil!
18 Sqn badge with Pegasus rampant
1960's Mobil Oil logo
lemonchiffon