The short version is that there are a lot of refugees fleeing terrible places, and a percentage of them will keep walking to get further and further from where they started. The majority of refugees fleeing to the UK are from Syria, and I think it's pretty self-apparent why someone would want to leave Syria.

Turkey gets the most refugees (because of geography), but they don't want a bunch of refugees, so they make it hard on them, and so some of those refugees keep moving, some aiming (for obvious reasons) for richer companies like Germany or France, and a fraction of them will keep going to the UK.

Individual stories vary tremendously, but imagine one country suddenly becoming REALLY shitty to be in, and millions and millions of people trying to get to anywhere else. You can imagine that the closest countries get the most migrants, further (but more desirable) countries get a smaller chunk, and even further countries get an even smaller chunk. But there are A LOT of refugees to start with, so a small percentage is still quite a lot.