Series-wound brushed DC motor. Yes, you can run it at around 240V DC, but a slightly less will probably do the same work with a bit better efficiency, because it will run a bit better on DC.
A bit of background:
An electric motor works by providing magnetic fields that pull each other together, or push each other apart. A motor has two parts, rotor and stator; both provide magnetic fields that repel of attract each other. By changing one of the fields with the correct timing, the rotation can go on and on.
A permanent magnet DC motor uses magnets to generate a constant field, usually the magnets are on the stator. In the rotor, windings generate the changing field; the brush assembly is responsible for providing the correct timings, energizing the windings in sync with the actual position. Now, if you reverse the terminal connections, the direction and the sequence of the changing rotor field swaps, and the motor runs the opposite way.
A series-wound brushed DC motor, on the other hand, does not use permanent magnets; both parts of the motor use windings. Furthermore, the windings in stator and rotor are electrically connected in series, so that the same current flows through both. Now, if you reverse the applied polarity, both magnetic fields swap their polarities, and the net result is the same as before. Such motors are widely used in older-generation electric vehicles (up to hundreds of kW), but also in practically all power tools, vacuum cleaners, etc.
Of course, when the direction of rotation is the same, swapping the polarity at 50 or 60 Hz just means high current ripple, causing torque ripple. These machines run smoother and better on DC, but they are designed to be "good enough" with direct AC input.
Why use brushed motors? The answer is simple; single-phase mains-driven 50 or 60Hz AC induction motors totally and utterly suck! Their power / weight ratio is disastrously bad, and the torque / weight ratio is even worse, torque vs. rpm characteristic means that they only provide torque near the rated full rpm, so can't be used in power tools where the mechanical load may cause the tool to run at reduced rpm; they "stall" and stop working.
If you need any torque out of an electric motor, you want to have at least two phases, i.e., dimensions of the magnetic field vector. An actual single phase machine is unable to start if it happens to be in the unfortunate position. In a 50/60Hz single phase ACIM, which actually internally is a two-phase machine, the second phase is generated using a capacitor, and it will never be at optimum 90 degree angle, and will be weak.
A vacuum cleaner with a 1 kW AC induction motor wouldn't be very portable, neither in size nor weight. A drill weighing 5kg is impossible to use.
A brushed motor is internally an AC motor, in the end; the windings are switched on and off to provide alternating fields. The designer can use any arbitrary number of "phases". The brushes are an old-school variable frequency drive, which apply correctly timed currents in the windings. This means, a brushed motor can use higher rotating magnetic field frequency, and are not limited to 50 or 60 Hz, so they are able to get beyond the 3000 rpm / 3600 rpm top limit.
Using higher rotating field frequencies means delivering the same power with lower magnetic field density, meaning less iron material needed for the same output power. It's the same reason why high-frequency SMPS supplies are used today instead of 50/60Hz transformers.
Of course, using carbon brushes is a very old-school way to do this, but it works, so whatever.
Expect to see a gradual change to electrically commutated permanent magnet AC motors, also called "BLDC", even in the cheapest things. At some point, the required MOSFETs, position sensors and driver ICs are cheaper than the carbon brush and copper commutator assembly.