As there are no parking restrictions anyone can park anywhere that cause obstruction to other road users.
Cones are meaningless - unless they are police or other authority cones - and can be moved. Thinking about it, there must be an offence committed by putting these cones on the public highway - littering, obstructing highway...?
It is obstruction to park on white lines that are painted across dropped kerbways. The police can act on complaints of obstruction from the householder.
Interfering with vehicles is obviously against the law - if there is the slightest hint of damage it could be criminal damage, otherwise it is a civil trespass.
Sadly, knowing your rights and entitlements is totally different from physically getting them.
Would it be possible to turn the street into a 'residents' parking area' where permits are required? This would cost, obviously, but should stop commuters parking.
Is it one household that is being awkward, or several? The majority?