Can you tell us what make of burner you are referring to? Myson used a number of variants, most common being Riello. Is the burner enclosed in a red metal box or is it "bare".
I'd make a stab in the dark that it's a bare Riello (same thing inside the red metal case if thats what you have).
If my guess is correct the burner sequence control is a grey plastic box on top of the burner unit. This box controls everything and contains the ignition generator, holds the flame detector photocell etc.
If the photocell has suffered heat damage or has gone short circuit the sequence control will "think" a flame is present before it should be and go through an abbreviated sequence to "false light lockout" No ignition spark will be produced during the run to lockout.
If you have a different model of burner the story will be slightly different so check and come back.
NB the photocell is a simple plug in unit. However if the problem began with an oil leak that needs dealing with pdq.