I don't agree with hunting foxes with hounds, and I'm dubious about the merits of shooting them, really.
However, I am horsey and have been on drag hunts and to other hunt activities and I wanted to clear up some misconceptions.
These days, there are a few different types of legal hunting:
Drag hunting- where the hounds and riders follow an organised pre-laid trail. This existed before the ban (since the 1800s) and the trail is usually laid so that people can have a fast, fun day out with lots of jumping. Some hunts also specifically lay trails where there is always a non-jumping alternative. Drag hunting is pretty much solely for the entertainment of the riders, and the hounds are there for tradition only- drag hunters would not usually want to go off after a fox (even if legal). They want the speed and thrill, rather than the kill and the hounds are trained to specifically follow the "drag" scent which is often synthetic these days.
There are also drag hunts that use bloodhounds to follow a human runner, although these are much rarer. This is sometimes called "hunting the booted foot" which sounds a bit sinister!
Trail hunting- This is what replaced fox hunting when the ban came in. Usually, an animal scent is used, but the trails are laid to try and mimic the behaviour of a fox, so it is a slower day and sometimes the huntsmen and riders do not know where the trail is laid. It was only invented in 2004 and viewed by many hunts as a "temporary" activity until the ban is lifted. In general, it is trail hunters who have "accidents" where foxes are killed, as their hounds are usually trained to follow live quarry. Trail hunts may go out with terrier men, with the intention of pursuing foxes underground.
I'm sure most trail hunts aim to stick to the law. I'm equally sure there's a few that don't.
"Legal" hunting- there are also some hunts that still go out with the expressed intention to kill an animal. They do this in a variety of legal ways or grey areas, such as flushing foxes to be hunted by birds of prey (bizarrely this is still legal). Some hunts use terriers, which is legal if done in a very specific way- AFIAK, more hunts now use terriers illegally on a regular basis than use hounds illegally (although of course they don't publicise this). The legal intention with terrier hunting is that the fox is flushed and shot, but often this isn't what happened. In Scotland, I believe it is still legal to flush a fox with hounds to guns.
Many hunts also organise fun rides, hunter trials, sponsored rides and so on. These are partly done as part of the country social calendar, and for sport (a hunter trial is like the cross country part of eventing, a timed event over fixed obstacles that horses and riders tackle one at a time). Fun rides and sponsored rides aren't competitive- there's usually optional jumping and people go to have a good day out and ride on land where they aren't normally allowed.
Although these events don't involve hunting as such, they are usually done in part to raise funds for the hunt. Personally, I wouldn't attend such an event if it was run by a hunt I knew to be regularly killing foxes but I can also see why people don't think too deeply about these and often such events won't make a big profit these days.
As with hunts, I think there are well educated and effective sabs, and sabs who have no idea and will just target anyone on horseback in the general area. I think anything done to cause horse and rider to part company is extremely irresponsible, due to the risk to the horse if it panics and the general public if it ends up on a road. I have seen videos of sabs doing things to horses/hounds that I would personally consider cruel.
I can understand why sabs can be tempted to violence- if the ban was better policed, then it would be less of an issue as they could just gather evidence and report to the police. Personally, I'd like to see whole hunts prosecuted rather than single individuals, as well as all the landowners involved- but I understand that this would be tricky to organise!