Since they enjoy it so much and you want them to go out, I think it’s a good schedule you’ve got as it is. Going outside is good for the body’s production of vitamin D, via the sun’s UVB rays. A couple of hours outside per week will give them sufficient vitamin D.
Other than that, going outside is good because it allows the bunnies to perform their natural behaviors (digging, grazing), but these benefits have to be weighted against the many dangers that lurk in the outdoors world. If you are in Europe you need to vaccinate your buns against myxo and RVD. In Australia there’s vaccine against RVD. In North America there are no vaccines, because you rarely see those illnesses there.

Since you are in the UK I feel morally obliged to issue a warning about a new strain of HVD called RVHD2 that now exists in the UK and in Australia (and probably in many more countries but we haven’t found any info except from the UK and Australia). There is a new vaccine available in the UK: RVHD2 vaccine

We just started a discussion about this yesterday: vaccine in Europe-thread

I would have preferred not to scare you like this, but since I now know about this strain existing in the UK, it just wouldn’t be right to not mention it. 

Please make sure the habitat is secure. PLEASE. If any animals like dogs get in, get it out immediately and grab your rabbit asap. Always supervise.

I have a galvanized rabbit run with a roof for when mine go out, which keeps them safe, catchable, and its easy to add shade and water.

My previous rabbit, Bunny, just loved to go outdoors. She particularly liked the front yard.  I’m very sure it was because there were so many things to watch, traffic, people walking by on the sidewalk, and also people walking their dogs.  There were some bushes near the sidewalk and she just loved to lay hidden there for the perverse joy of having dogs walk by only a few feet away and not notice her!  She was never out by herself, always my wife or me were nearby.  Usually, she was out for 1/2 hour or so, since it could be a little booring to watch her.   In the morning, I’d take a cup of coffee and the morning newspaper to wile away the time.  She was pretty obedient, she learned not to go in the neighbors yard, since I would always shoo her back to our property.  She was pretty good about going back into the house.  Sometimes I had to use what I called my rabbit wrangling stick.  She would often be behind bushes where I couldn’t reach her so the idea was to push the stick into the vegetation and give her backside a push towards the house. Of course, I never hit her, just a gentle push. Sometimes she like to have me chase her before she decided to run back into the house.  We always kept the front door open when she was out.  If she became scared which she occasionally did, she would run back into the house.  The front door was in effect her bunny hole.  

My current rabbits, nearly 7 months old, are not yet interested in going outside.  I set them on the stoop in front of the front door, they do seem to be interested in looking at street scenes for a while, but then run back into the house.  I did get Flemish rabbits with a goal in mind of being able to leave them in the back yard sometimes on their own with the back door open.  They’ll big enough that a feral cat shouldn’t bother them.  I have had both of them microchipped.  

Unless it’s rainning heavily or there’s a snow storm, my rabbit goes outside from 7-8am and comes in around 6pm. I’ve trained him to wait at the door when he wants to come inside, so the door is always closed. Of course, rabbits love being outside, but if you can’t let yours out more, don’t feel bad. Most domestic rabbits aren’t even allowed outside at all.

However, for your fence, I don’t know what it’s made of, but make sure the metal is fairly thick. My first fence was a regular wire fence, but he chewed through it. I had to change it to a thicker wire fence that he can’t chew.