Don't be concerned Baruk.
You couldn't submit P60 as they don't get issued until after the Year-End tax declarations.
P60 is not designated as mandatory by UKVI
Here's the instruction:-
......In addition to the evidence listed above, paragraph 2A of Appendix FM-SE specifies that
P60(s) for the relevant period(s) of employment (if issued) and a signed contract(s) of employment may also be submitted in respect of paid employment in the UK.
If they are not submitted, the decision-maker may grant the application if otherwise satisfied that the requirements of Appendix FM-SE relating to that employment are met, or they may ask for the documents to be submitted in accordance with paragraph D of the Appendix. [/B]
Hope that puts you mind at rest. Your P60 would not have covered the relevant period of employment.
I highlighted the key issues.