There goes the neighbourhood: 'The Blairs ought not to be living here...'

They may seem to be the ideal neighbours - a wealthy, well-connected, law-abiding, middle class couple with four children, not given to drinking heavily or holding wild parties, whose mere presence reduces the risk of street crime by drawing extra police to the area.

But even before Tony and Cherie Blair have taken up their new home in Connaught Square, near Marble Arch, relations with other residents are promising to be almost as difficult as with their current next-door neighbour in Downing Street.

Officially, tomorrow is the day that the family will leave the flat above 11 Downing Street, which has been their main home for 10 years. Removal vans have shifted most of their belongings, many of which are now in a warehouse in Brent.

Meanwhile there is still an army of builders, electricians, plasterers and security counsellors putting the finishing touches to the elegant new Blair residence. The mews house at the back, which the Blairs have also bought, is marked by scaffolding covered in tarpaulin.

The ground-floor room, which looks on to the square, was completely empty yesterday, apart from a woman in a smart suit conducting endless negotiations over a mobile phone.

What has alarmed the residents of the square is the extraordinary precautions underway to ensure that the former prime minister and his wife are protected from anyone who may be contemplating revenge for the war in Iraq or over some other grievance.

If the Blairs are really that much at risk, the neighbours say, someone should tell them for their own sake that it is not a good idea to be living in a crowded part of central London. On the other hand, if the risk is low, life in Connaught Square is being disrupted for no good reason. A petition has been passed around the Square pleading for help from Westminster Council. It says: "It has been suggested that to protect the Blairs it may be necessary to prevent vehicles and unauthorised pedestrians entering the west side of the Square, run part of the Square into a gated community, policed by armed guards, prune or cut down some of our magnificent old plane trees [and] have a police helicopter hovering above the Square."

The petition adds: "If the risk to the Blairs is so great, the security services should advise them that they ought not to be living here. If it is safe for them to live here, they should not need anything like the level of security that has been suggested."

The police said yesterday that they plan to meet residents in the hope of allaying some of their concerns. A Westminster Council spokesman said: "Once we have received the petition we will put it through the due process, which is to contact the ward councillors and ask them to bring it forward to full council."

Westminster Council also has to make a judgement on a separate dispute about whether the alterations planned by the Blairs to their Georgian home, including a roof garden and solar panels, will spoil the look and the general environment of Connaught Square.

Property developer John Larkey, who lives next door, has complained that noise from the children's bedrooms on the upper floors of the five-storey house would be "disruptive" and that if the couple held barbecues in their roof garden, the smell would be a nuisance. Residents have also objected to the proposed solar panels, which they called a "fashion accessory", and to the CCTV cameras.

Builders have knocked through the wall adjoining the two houses, and are converting part of the ground of the smaller property into a shining new kitchen. The demolition work is almost complete.

The builders hope that they can be finished altogether in about another two weeks. Meanwhile, Gordon Brown has told the Blair family that they can continue for the time being to use Chequers, the Prime Minister's grace and favour home in Buckinghamshire.

The Blairs have not been lucky in the property market. They seem to have less of an eye for a bargain than many others dabbling in the top end. Madonna yesterday snapped up what is believed to be the sixth London home that she owns. The singer and her family live in a £7m, eight-bedroom home in Marylebone. Now, she has paid £6m for the 10-bedroom Georgian house next door, which has six floors and an artist's studio. The house belonged to the designer developer Paul Davies, who bought it last year for £3.6m. He has the reputation of having a golden touch, making headlines recently by renting out one of his Mayfair properties for £40,000 a week. A source said: "Madonna knows that when Paul Davies moves into the area it means prices are going to rocket. She said she wanted to buy the whole street."

The Blairs, however, made an expensive decision in 1997 to sell their Islington home, because it was not secure enough for them to live in and they did not want the problems of renting it out. Cherie's first venture back into property ownership, when she bought two flats in Bristol, brought nothing but grief because of the involvement of the convicted con man, Peter Foster, whom she knew through her style adviser, Carole Caplin.

The family bought the Connaught Square property for £3.6m in 2004, setting off premature speculation that Mr Blair was on the point of handing over to Gordon Brown. The couple hoped to rent out the house for £4,000 a week, but had to settle for substantially less. They bought the mews house at the rear for £800,000.

All was quiet in the square yesterday, except for the clatter of workmen. One uniformed officer was on patrol in front of the Blairs' new home, and another in the discreet mews at the back. A notice on the door of the house next to the Blairs' warned: "No reporters". The people of Connaught Square have suddenly attracted the curiosity of outsiders, and they do not altogether like it.

Connaught Square, London W2

* MP: Mark Field (Conservative)

* FAMOUS RESIDENTS: (past and present)

Paul Oakenfold, the multimillionaire DJ

William Orbit, record producer

Claudia Winkleman, television presenter and Independent columnist

Eric Mouilleron, entrepreneur

* HOUSE PRICES: Average house price: £1,411,710 - based on sales over the past three years. You can buy a two-bed flat for £445,000; and a six-bed house for £3.5m.

* SCHOOLS: Connaught House School;

Lansdowne Independent Sixth Form College; Maria Montessori School, Bayswater; Pembridge Hall School.

* IMPORTANT BUILDINGS: St John's church (Hyde Park Crescent), Tyburn Convent (Bayswater Road) and the Diana Memorial Fountain (Hyde Park) are all nearby.

* EATING AND DRINKING: The Carbon Bar offers cocktails and Ibiza-style tunes. Locanda Locatelli has fine Italian food by celebrated Giorgio Locatelli; Maroush is a Middle Eastern local complete with belly dancers; Cafe du Liban, a Turkish bistro; Café Quebec, "light breezy Indian"; and the square hosts an annual summer party organised by residents.