These regulations, which were enacted in 1983 (Statutory Instrument No. 1168), defined a new type of vehicle under the Road Traffic Acts. Other legislation says who is permitted to ride an EAPC (anyone over the age of 14), where they may ride it (not defined, but presumed to be anywhere you can ride a normal pedal cycle) and how they ride it (just like a pedal cycle). See the pages on Construction & Use  and Lighting  regulations for more about that. The Electrically Assisted Pedal Cycles Regulations simply set out the minimum criteria such a vehicle must satisfy – or else it will be regarded as some sort of electric motorbike (taxed, insured, used only by a licensed, helmeted rider etc.). These criteria are as follows:
- The vehicle must not weigh more than 40 kg if a solo bicycle, or 60 kg in the case of a tandem or tricycle.
- The vehicle must be fitted with pedals, by which it can be propelled.
- The vehicle must not be fitted with any sort of motor other than an electric motor.
- The continuous rated output of the motor must not exceed 200 watts if fitted to a solo bicycle, or 250 watts in the case of a tandem or tricycle.
- The motor must not propel the vehicle when it is travelling faster than 15 mph.
Not included in the above list, but required by Construction & Use regulations  (so they ought to be listed since you can't legally use the thing otherwise!) are the following additional criteria:
- The vehicle must be fitted with a plate (where you can easily read it) showing the manufacturer's name, the nominal battery voltage and motor power output.
- The power switch or control must default to off, requiring a constant intervention from the rider in order to maintain power assistance. (No power without pedalling, as required in some other countries, also satisfies this requirement.)
Note that these definitions do not include cycles with more than three wheels. So you cannot electrically assist a quadricycle without it becoming some kind of motor vehicle.
Vehicle weight, for the purpose of these regulations, is the weight of the cycle without a rider and no load other than 'the loose tools and equipment with which it is normally equipped'. Nominal battery voltage and continuous rated output are defined with reference to BS1727: 1971. Apparently this lets the peak output be a little higher than the number of watts specified above.
Many other countries also allow a modicum of electrical assistance on pedal cycles, under similar but slightly different regulations of their own. Mostly they allow a bit more power (250W rather than 200W), with a fractionally higher motor cut-off speed of 25 kmph (15.5 mph) and up to four wheels. On the other hand, most countries additionally require that the motor must not propel the vehicle when the rider is not pedalling. This no power without pedalling type of EAPC is called a 'pedelec', as opposed to an 'E-bike' that will also go when the rider freewheels. I think that British experience proves that a speed limited motor is enough to keep an E-bike behaving like a pedal cycle, but other countries are insistent that the rider also pedals.
In 2004 a European Directive harmonised 'type approval' procedures for motorcycles whilst making an exemption for electrically assisted pedal cycles. Type approval comprises technical safety tests that a motor vehicle has to pass before it can be put on the market. Like the Pedal Bicycles (Safety) Regulations , these tests are of concern to the manufacturer and retailer and not something the customer or user ordinarily has to bother about. The EAPC exemption is based on the majority European definition of an EAPC, i.e. a pedelec. So all E-bikes now have to go through motor vehicle type approval before they can be sold in UK, including those that can be used just like pedal cycles once the customer gets them out of the shop. So there's not only a bigger market for pedelecs, they are also easier to put on the market, here as well as abroad. No power without pedalling is no problem for most people (except the very infirm), but some of these machines are slightly over-powered, up to a speed fractionally higher than UK law permits to be used – without all the paraphernalia of a motorbike. Fortunately, the police do not take any notice of this minor technical infringement and it seem likely that UK regulations will eventually be brought into line.