I popped down to Brighton today with an off-peak open return for £19.05
I thought this was quite good because I got an online discount, so it was cheaper than the standard price of £21.90

When I changed trains at East Croydon I met my brother who had traveled down from North London. His ticket from Blackfriars cost him £15.50

Checking the prices it is cheaper to buy a standard open return ticket (without online discount) from Forest Hill to East Croydon and then another from East Croydon to Brighton - total cost £18.90. The only difference is that you must travel on First Capital Connect services from Croydon to Brighton (leaving 3 minutes after the Southern service - 10:11am rather than 10:08am). These trains take exactly the same time to get to Brighton, so you arrive all of three minutes later. But the combined ticket is not available on any online site, you have to buy the two separately.

To cut the cost further you can use PAYG Oyster to East Croydon, which takes the total cost down to £17.70, you just have to remember to swipe out and in when you change at East Croydon.

So what would have actually been cheapest for me?
Not the £19.05, not even the £17.70, but because I have a season ticket to London, I should have gone to London Bridge (free) and get the First Capital Connect train from there for just £15.50. It would have taken longer, but not as long as it takes searching for the cheapest rail fare.