No, unless you administer the public space or are acting in the interests of safety (e.g police officer, gas utility worker). All public space is owned by someone; usually a local government.
You can use the space by e.g putting out a picnic blanket, even a very (but not absurdly) big blanket. The law does not prevent anyone from sitting on your blanket, however, social convention does and this can be more potent than the law.
If your use of the space impedes others use then they may complain to the administrator of the space (or the police); if they were to give you a lawful and reasonable order to stop doing whatever it is that was complained of and you didn't then you would be trespassing.