When I'm flying from my airfield, I usually am out of range of the airfield's radio within 50 miles or so, at low altitudes. How does the emergency frequency (121.50) work? Where is the location of the tower and how do you speak to someone if you're not in range of it?
You're out of range of you airfield radio operator on the frequency they are tuned, but you almost certainly not out of range of all radio operators.
In the UK, there are military units, LARS, area controllers and towers at bigger airfields as well as all the commercial airliners all tuned to 121.50.
As wikipedia says:
In the UK, 121.5 MHz is monitored by the Royal Air Force Distress and Diversion cells (known as "D&D") at the London Terminal Control Centre and the Shanwick Oceanic Control, from a nationwide network of antennas. Depending on the aircraft's altitude and location, the personnel in the centres may be able to use triangulation to determine its exact position which can be useful to the pilot if the aircraft is lost or "temporarily unsure of position".
So there you have it, there are a network of antennas which will cover you wherever you are.
Besides pretty much every ATC ground station, on airliners, with 2 Comm radios, normally Comm 1 is used for all ATC 2-way communications, and Comm 2 for ATIS, talking to Company ops, possibly air-to-air, etc. When not used for that sort of stuff, it's normally set to Guard (121.5), esp over sparsely settled areas or areas adjacent to or in the middle of oceans.
So in your case, airliners on arrivals and departures probably won't be, but those passing overhead UK to or from the North Atlantic Tracks will probably have Comm 2 set to 121.5 and if you broadcast a Mayday, one is likely to answer if in range.
I once arranged rescue, after being forced down by engine trouble on a random lake in the Canadian wilderness, by raising an airliner on Guard with a PAN call when I saw its contrail overhead.
At airports with a control tower, the antennas are located on the airport—on top of the control tower itself or on a dedicated (and relatively short) radio mast elsewhere on the field. As you have found, control tower equipment is not designed for long-range communication. It doesn't need to be.
The trick with the emergency frequency is that it is the same everywhere. Usually the authorities try very hard to assign radio frequencies for various ATC units and functions to ensure that transmissions from pilots will not be received by more than one ATC unit, and if there are problems a new frequency will be assigned instead. The Guard frequency is exactly opposite: every ATC unit which monitors Guard monitors and can transmit on the same exact frequency, 121.5. This means Guard is not ideal for routine communication—every time you transmit you will be coming out of speakers in several different buildings, only one of which needs to be hearing you—but perfect for emergency communication, when you need to talk to somebody, anybody, right now.
Radar control facilities often cover far more airspace than can be reached by a single antenna site, so they will have remote antenna locations and audio signals will be carried back and forth along telephone wire or similar methods between the remote antenna and the control building. When necessary to ensure coverage, an antenna dedicated to 121.5 will be included at the remote site.