Geri Horner has been accused of disrupting phone signals in her village by building a barn for 14 horses.
The former Spice Girl knocked out local mobile reception by erecting the sizable corrugated steel shelter at her country estate, her neighbours have claimed.
Locals also said that Geri, 50, and her husband Christian Horner, the Formula One boss, have "re-routed public footpaths" and that their horses have been a "menace" to the public.
Despite the objections, the celebrity couple have now been granted part-retrospective planning permission for the scheme, which was already under way in the rural home near Banbury, Oxfordshire.
However West Northamptonshire Council, who gave permission for it to go ahead, were criticised for ignoring the strength of feeling in the village. Residents accused it of caving into the demands of wealthy constituents.
One letter of objection said: "The barn has affected mobile phone signals in the village without a doubt."
The letter added: "No notice of planning permission notices ever erected in retrospect or any planning.
"The barn is hideous, totally destroys the landscape and views. Excess floodlights all night long causing light trespass to all neighbours from the main house also.
"What is it with this council - do they cave into the rich because they don't have money to fight them in court?
"Many people in the village not happy at all laws being allowed to be flouted. They have even re-routed public footpaths and installed their own style gates, how on earth is being allowed?
"Their horses are also a menace on the footpaths to the public.
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Another neighbour added: "The barn affects mobile signals in the village, is a hideous blight on the landscape and does not conform.
"If this build is retrospective, why is it still being built? There is now a huge glass construction being built on the end of the barn - don't the council care of the favouritism being shown to the wealthy here? Unacceptable.
"This is not a verbal attack on the rich, this is a breach of fairness to all. Favouritism is being shown here."
Others said the proposal should be rejected due to the strength of local opposition.
One said: "Rishi Sunak PM stated in the last few days that any village that wholly objects to building plans, such as those happening without council diligence at Glebe House, are to be refused if the local village residents strongly object. Which they do."
Planning documents say the old barn "is being replaced with a new barn of the same form and scale with stone plinth walls, timber cladding (Cedar) and a corrugated metal roof."
Ms Horner married the boss of the Red Bull F1 team in 2015 and the couple have set up home in the Oxfordshire countryside.
Based in Marston St Lawrence, near Banbury, Ms Horner has often showcased the many animals on the country estate, including donkeys and chickens, on social media.
Her current image is a far cry from her 90s persona, when the Spice Girls were at the height of her fame as she wore a short Union flag dress.
A keen horseman, she celebrated her first winner as an owner - with a horse named after her hit solo single, Lift Me Up - in May.
The council said permission was granted on the condition it was used for "private equestrian and land management uses only" and "no commercial use, including riding lessons, tuition, livery or competitions shall take place at any time".
Restrictions around external lighting were also imposed.
The council officer said: "West Northamptonshire Council always seeks to look for solutions rather than problems so that applications for sustainable development can be approved, thereby resulting in improvements to the economic, social and environmental conditions of the area."
Mrs Horner has been approached for comment.