Hardknott OnTrack, for instance, does not have any handpulls, but does serve cask beer. Some pubs serve cask beer by gravity. I know of a few bars where cask beer is actually served through taps, much like keg beer. This does not stop it from being cask beer.
The handpull was a good way of getting beer out of the cellar and up to the bar, before the days of new fangled electric pumps and the like. It works well with a pub where the cellar is directly below the bar. Have a look at the picture I drew1. The handpull "sucks"2 beer up to the bar through good old fashioned beer hose. It's simple.
Many, and I do mean many pubs have no such arrangement. The beer hose can hold quite a lot of beer if it has any length. It is difficult to keep the beer in the pipe cool and there is significant wastage when line cleaning etc.
Most pubs have installed a thing called a python. It is especially useful where the cellar is not directly below the bar and where there might be some distance the beer has to travel. Suppose it is a more modern building that has a solid concrete floor and the cellar is a little way away on the same level. A python is a bundle of pipes, lagged and kept cool by a circulating cold water cooling system. The pipes are a lot narrower and so the wastage is less.
The problem with this is that the resistance to the flow of beer is much greater. Using a handpull with longer narrower pipes would at best be difficult and at worst pull the CO2 out of the beer.
This is solved by having a sort of servo pump in the cellar to pressurise the pipe. It's normally a FloJet diaphragm pump. The beer in the pipe is under a pressure all the way to the bar, a bit like kegged beers.
This is all well and good, only handpulls won't stop a pressurised beer from flowing, this is not what they are designed to do. Just before the handpull is installed a check valve. Basically this detects the reduced pressure caused by the "suction" from the handpull and so opens allowing the pressurised beer into the handpull.
This effectively makes the handpull act like a valve, rather than a pump. Its significantly faux and over complicated.
Those of us who are sensible omit the handpull and check valve and just put a tap in its place.
1I didn't draw the figures. These came from Brains during our recent collaboration3. I'm not sure who they are supposed to be.
2 Actually, it doesn't suck at all, it's atmospheric pressure that pushes it up. All my old physics teachers and lecturers would now, quite rightly, be shaking their heads at me for using such a stupidly non-scientific word like "suck" - however, I like to think that handpulls suck.
3More on this later, promise.