Hazards
I believe the main issue is that they can get warm if you don't fully extend them and then draw a high current through the coiled wire.
See Leads & Extension Lead Safety
RCD (Residual-current device) or GFCI (Ground Fault Circuit Interrupter)
Most advice is to use an RCD with extension cables over 15m. I use a plug-in RCD. You can buy replacement outlets(wall-sockets) that incorporate an RCD.
I suspect this advice is simply because the length of cable increases the likelihood of accidental damage to the cable (spades, shut in doors, etc)
Voltage drop
The voltage in the UK is nominally 230 V with a tolerance of +10% to -6% (in much of the EU it is +/- 10%) - In practice most wall outlets are likely to be at 240V as this is the standard voltage prior to EU harmonisation and is within the tolerance.
This means that equipment must be able to work with voltage as low as 216.2 V.
If plugged into a 240 V wall outlet, your 50m cable would have to lose nearly 24 volts before it dropped to a level below the UK tolerance in supply.
That means, at 13A and 50m the voltage at the end of the cable would be OK so long as the cable had a resistance of less than 30 mV per amp per meter. This means you want a copper cross-sectional area of at least 1.5 mm². Ref, Table
The details for your specifc product don't mention the conductor size so you can't do the calculations for yourself.
You can check the voltage drop easily with a "kill-a-watt" type device or a suitable multimeter or voltage-tester rated at least Cat-II 600. If the drop is too high you have the statutory right (in the UK at least - SOGA 1979) to return the cable as unfit for purpose.
Generally, when voltage is low, appliances stop working or work poorly (dimly, slowly or intermittently) in most cases this wont cause a hazard.
For a 200A residential service in the US or Cananda typical would be 4/0-4/0-2/0AL or 2/0-2/0-1/0CU conductors. Either combination would normally be run in 2" conduit.
This is only scratching the surface of what you need to know to do this project. Are you aware and knowledgeable of all the other requirements/codes/etc???
Best Answer
To directly answer your question: what you want is a "voltage regulating transformer". Alternately, I have also seen the wording "voltage regulator converter transformer" - basically add "transformer" to the search terms you're already looking for.
The issue is, in order to counter the voltage drop, you need to start at a higher voltage, so you need a transformer before the regulator. Likely you will need a 240/120 V step down transformer (most common). In theory there could be a 110V/120V+ step up transformer that will do a slight step up before the regulator so the regulator can regulate it down - but I can't find a specific commercial device that does that. Hopefully there's a 240V plug available to you, as well.
That being said, you should take the comments that have been made into consideration. It's likely much cheaper to just get a thicker extension cord (especially consider you'll probably at least need a new 220 V cord for the transformer anyway). The bigger the conductor cross-section, the less voltage drop per foot you'll experience. You can do the calculations to figure out what size you need, I suspect 10 AWG as was suggested will probably be sufficient for 200 ft.