Have found my answer - maybe this will help another family.
Originally, when I went to price on the website, I priced for just one ticket. That was (best price, being off peak) 31.70 GBP.
I (erroneously) thought our trip for 6 would be ~ 180 GBP - putting it out of our budget and almost axed that part of our trip.
However, I decided to put in all of our family members. When I put in our whole family, which was 3 adults and 3 children, I got round trip fares for all 6 of us - same journey - for 66.40 GBP.!!
It automatically changed one child to an adult and applied "GroupSave". Four of us (as adults) are now travelling at 63.40, which looks like buy one-get-one free adult fares, and the other children are $1 each.
Strangely enough, 2 adults and 2 children under 16 returns a higher fare of 95.10 GBP.
So - it looks like they are heavily discounting for larger families.
I got a similar discounted fare to go to Windsor. Again, the website recalculated everything automatically.
Also - you can select your seat.
Finally, another thing I have learned is that they will show both legs of the journey and call one "outbound" and one "return." Then, it gives the price for the "return" trip. This was very confusing to me - and I was afraid the price being shown was only for the one-way return. Today I e-mailed someone at our hotel who explained that "return" trip means "round-trip."
I mention all of this because I found the website to be non-intuitive, to say the least.
Happy travels.
Kathy