Catherine and Nick Bennett say they have suffered sleepless nights after constant late night parties at Sharon Sprakes's home.
Since 2006 the Bennetts have complained to Portsmouth City Council about her behaviour and have kept a log of more than 300 separate incidents since she moved into Woodhay Walk, Leigh Park.
This led to Mrs Sprakes being hauled before Portsmouth County Court. But instead of evicting her the city council asked the court to impose a demotion of tenancy – a lesser penalty which takes away some of her tenancy rights.
Under the order, the 39-year-old, who has convictions for being drunk and disorderly, possessing drugs and assaulting a police officer, may be evicted if she continues to behave in the same way.
But Mrs Bennett, 35, who has been on long-term sick leave from her job as a learning support worker, said this wasn't enough.
'This has made our lives a misery and it has gone on too long,' she said.
'When she moved in it was very loud and there would be shouting and drunken fights outside the flat. People are banging on the door at all hours.'
The couple say they are now leaving the street.
Mrs Bennett added: 'I can't understand why the council lets people who destroy the place stay and we are driven out. It seems unfair.'
Portsmouth City Council says it followed the correct procedure and is looking to rehouse Mr and Mrs Bennett.
Gerry McDougall, the council's housing management's anti-social behaviour manager, said: 'We've considered all the circumstances and have taken the most appropriate course of action.
'If there are any other incidents over the course of the next year we are entitled to take further action.'
FACTFILEDemotion orders are used by local authorities as a way of controlling anti-social behaviour by tenants.
Landlords can apply to the county court.
Once granted, the tenancy is replaced with a less secure form of tenancy.
The court makes the order if the tenant, or another visitor to the home, has behaved or threatened to behave in a way causing a nuisance or disturbance.
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