No, they can't, for the same reason that front doors in the UK are so often compelled to open inwards, even WOPR's wholly correct Comment, above, is almost irrelevant.
Opening a gate, door or anything else across a pavement isn't simply 'taking space'. It is by definition obstructing the pavement.
Whether this particular pavement is a public right of way is what matters, and that's a different question which depends on the particular circumstances. Still, in almost all cases, the pavement will be a public right-of-way.
For a pavement or any other path- or roadway not to be a public right-of-way would require the owner to post prominent notices saying so; saying, for instance, 'Private path/road. No public access.' Not immediately but eventually, failing to post those notices would automatically give the path or road public right-of-way.
In some cases, that rule is so strictly enforced that the posted notice will state '… and the public are allowed to use it until further notice…' and that 'further notice' will mean the owner closes the road for at least one day each year.