Permitted transmitted power levels
A directional antenna is particularly useful to anyone trying to extend the reach of their WiFi because it improves reception quality: it not only strengthens the signal coming in on-axis, it also equally attenuates off-axis signals. This masks out a lot of interference very effectively.
In the UK Ofcom (The Office of Communications) is responsible for regulating the use of the electromagnetic spectrum. According to their regulations, in the IEEE 802.11b/g (2.4 GHz) WiFi band, maximum equivalent isotropic radiated power (EIRP) must not exceed 100 mW. This means that a directional antenna must not radiate more strongly in any direction than a non-directional antenna with a spherical characteristic, fed with 100 mW.
Most WiFi modules only output between 30 and 50 mW, and this is further reduced by losses in the cables going to the antenna. According to our measurements, a typical directional antenna radiates so well that, with 50 mW at the WiFi module, somewhat more than the permitted power is radiated by the aerial. Many WiFi routers have a configuration setting that allows a choice of transmit power levels. If you can choose to reduce output power by half, you'll be on the safe side. Otherwise any interference you might cause could induce the neighbours to complain to Ofcom, who could then send a testing crew around and perhaps charge you with an offence. The transmitted power can also be reduced with a longer antenna cable, but that also impairs the received signal.
In practice, using a directionally radiating antenna is likely to benefit your neighbours because, since your transmissions are directional, interference is reduced.