The red squirrel is a protected species in the UK and is included in Schedules 5 and 6 of the Wildlife & Countryside Act 1981 (WCA) (amended by the Countryside & Rights of Way Act 2000). It is an offence to intentionally kill or injure a red squirrel or intentionally or recklessly damage or destroy any structure or place a red squirrel uses for shelter or protection, or disturb a red squirrel while it occupies such a place.
Therefore you must be very careful about when and where you fell any trees. See the section on felling advice for more detail.
The grey squirrel is regarded as an invasive non-native species following its inclusion under Schedule 9 of the WCA. Grey squirrels are also listed in the IUCN international list of 100 worst invasive non-native species. This highlights the damage that grey squirrels cause to our native flora and fauna; a problem severe enough to be recognised at a level of global significance. As such, the grey squirrel is regarded as a pest species and is afforded no protection under the WCA. Under Schedule 9 of the WCA, it is illegal to release a grey squirrel into the wild, or allow one to escape.
This means if you trap one, you are obliged to humanely dispatch it. You must not let it go as this act would be illegal.
Anyone who carries out, or knowingly causes or permits any of the above acts to occur could be committing an offence.