The play park, in Titchfield, was built in an MoD housing area to enhance the estate for families.
Deborah Queen, who lives opposite the park on Eastway road said: ‘We were told by our solicitors when we bought the house that it would never be built on.
‘None of the residents were informed that this was going to be built, even the MoD residents weren't informed so they’re all quite furious about it.
‘It is causing no end of problems, noise levels, the litter, people coming through from adjacent estates, parking, they’ve damaged all the pathways and the kerbstones when the contractors built it.
‘We’ve got a resident that’s in an MoD house and the park has been built less than 6 metres from his house, he’s lost all his privacy, he said the noise is just awful.
‘There just seem to be no consideration for the residents in the area, not even a courtesy letter through the post saying this is what we’re going to be doing.’
Last month the MoD came under fire for starting work on a play park in Tortworth Close, Fareham, before getting permission. Work stopped abruptly on this after concerns were raised.
Fareham Borough Council was not aware of the installation and has contacted the MoD to determine the best way forward.
Council leader Sean Woodward said: ‘The MoD obviously have their use of defending the country but building play-parks without consent or consultation is not good.
‘When we put one in as a council we consult the neighbours, the children we make sure we’re putting in what people want and we always bear in mind concerns.
‘The MoD just sort of sticks in what they want where they want and then of course there are consequences.’
An MoD spokesperson said: 'Unfortunately, work commenced to build the play park in Titchfield Park prior to securing the necessary approvals.
'Contractors are liaising with the local authority to explore retrospective planning permission and if this is not granted the play park will be removed.
'We are reviewing our processes to ensure that planning approval is undertaken where required for all new play park infrastructure in future.'