Given that you're travelling on separate tickets, there is little or no chance that the unnamed first airline will (or will be able to) check your bag through to A3. And given the frequent chaos in LHR, I certainly would not personally risk having a bag sitting unattended somewhere airside all day, waiting to make a transfer to Aegean. They are not expecting you to have a bag in transit to them, and they know nothing about your bag...this raises the chances that your bag will go missing.
A3 do not have an all-day check-in desk open at LHR. The desks appear to open around 2-3 hours before each flight according to this other related thread:
Checking bags early at LHR
There are left-luggage facilities that will store your bag for the day, or for however many hours you want to be free to go and explore London:
https://www.heathrow.com/at-the-airp...s/left-luggage