In 2015 a new ‘Good Samaritan’ law (‘SARAH’ - Social Action, Responsibility and Heroism Act) came into effect in England and Wales. See: https://www.legislation.gov.uk/ukpga/2015/3/contents/enacted
This act seeks to counteract the growing perception that people risk being successfully sued if they do something for the common good – like leading a school trip, organising a village fete, clearing snow from a path in front of their home or helping in an emergency situation.
There is no law preventing you from clearing snow and ice on the pavement outside your property, pathways to your property or public spaces.
It is very unlikely that you would face any legal liability, as long as you are careful, and use common sense to ensure that you do not make the pavement or pathway clearly more dangerous than before. People using areas affected by snow and ice also have a responsibility to be careful themselves.