Just get your father to apply online for a Non-O retirement (over 50) Visa as he will then not require proof of onward travel at check in, gets stamped in for 90 days and does not need to visit Immigration at all during his stay. The UK cost is £60 then nothing more to pay (the online TDAC arrival card is free).
The Immigration Officer holding your passport is the only one who can answer that as he will be looking at your complete stay history as well as your overstay