TL;DR version: direct flights with BA (not Aer lingus, american airlines, etc.) booked from BA.com get discounts off the airplane ticket when booking a free car in the checkout process - must click "view all car goups". You don't even need to use/pick up the car.
I found a 'travel trick' I thought I'd share in case it's useful to anyone. Some may have heard of it, but it was new to me and I don't think everyone knows about it.
Ok, here we go
I was looking for a flight to the US for a work conference, and had to stay below a certain budget. I tried flights.google.com and skyscanner, but both showed results from third party agencies with terrible trustpilot ratings and horror stories. Having been burned by a third party agency before, I decided I would only book directly with the carrier so that if I needed to make any changes I wouldn't be charged ridiculous fees.
I had to get from London to Portland or Seattle, and preferred a direct flight (not possible with Portland). When looking at my dates the cheapest offer was 872 quid. Clicking through the bookings pages, I saw "save $ when booking a car" and clicked "view all classes" (of car). Well it turns out that by doing that the ticket went down in price to 690 quid AND it came with a free car from Avis for 4 days. I needed a car anyway, so it worked out even better for me. All in all, I stayed in budget, and don't need to go out of pocket on anything.
Out of curiosity, I tried this "trick" on a few other routes, and it seems like as long as it's a direct flight through British Airways (not any of their partners) you can get a discount between 90-200 quid and you don't even need to use the car. You print out a voucher to use with Avis, so they don't have your reservation or credit card on file.
Ps you can also get avios points doing this, and I got bonus avios points for the car rental.
Hope it's helpful to someone! Best of luck