The threat to arrest for obstruction is widely used by the police at demonstrations.
Under the Police Act 1996 s89 it is an offence to assault, resist or wilfully obstruct a constable in the execution of his/her duty.
Willful obstruction of a police officer means doing any act which makes it more difficult for the officer to carry out their lawful duty e.g. stopping them doing something, de-arresting someone, deliberately misleading them, or giving a false name and/or address.
Being limp makes it more difficult for a police officer to move you, and is not obstruction.