Noone thinks you are mistreating him, don't worry. I know you care because you are asking and taking on advice - you would only be mistreating him if you refused to accept our advice and carried on regardless. So don't worry
Google is telling me British Giants are 5.5-7kg, so that is a very big bunny! It would be good if you could find out his weight, as a rabbit's weight should be monitored anyway as a general health check.
I'm afraid I have no experience of keeping giants, but personally, if I was to have a setup for one that size, I'd go for at least 10ftx7ft run. The 4ft height I think should be fine, but again I'm not sure how high a rabbit that big can binky.
Personally, I have a large rabbit who is 3.65kg, paired with a 2.2kg bun, and they have 48sqft (an 8ftx6ft run) and I find that, because of the 3.65kg bun's size, he cannot really build up speed in it, or have a real run around. It takes only about 4 normal hops for him to cross the entire run. (It was only meant to be temporary and they will be moving inside as soon as I can get a better job and move house.) Your bun will be around twice the size of mine, so you want a much bigger run than I have, really. Some time free-ranging every day would be good, is that possible?
Bear in mind that, whilst you can bring him in during the summer, the temperature change from outdoors to indoors in the winter could cause health problems and stress, so that wouldn't be an option in the winter.