London's mass cycle hire scheme is to expand into new parts of the city following a first year of operation which saw more than 6m journeys using the distinctive, blue-and-grey bikes.

The expansion was announced by London's mayor, Boris Johnson, at an event before this weekend's anniversary of the scheme, modelled on similar systems in Paris and elsewhere, and the biggest public cycling project in the UK.

The London version was launched amid gloomy predictions of possible indifference, mass vandalism and theft, and likely carnage as many thousands of inexperienced, helmet-less cyclists took to the capital's busy streets.

More or less all of these have been prove wrong. Bike use has peaked at almost 30,000 trips a day, and while there have been a small number of minor injuries to users the scheme has, as yet, experienced no major accidents.

This has happened even amid regular grumbles about the computerised docking station system, run by outside contractors Serco, which has been plagued with gremlins.

Thursday's announcement will see the bikes spread west and south-west, into parts of the boroughs of Wandsworth, Hammersmith and Fulham, Lambeth, and Kensington and Chelsea. This will happen within the next two years, funded in part by an extra £25m from the scheme's sponsors, Barclays.

By next spring, there will be an initial westward "spur" expansion to reach the massive Westfield shopping centre in Shepherd's Bush, financed in part by £4m from the centre's operators.

Johnson marked the anniversary with a press event at Westfield, riding one of the bikes around the shopping centre's main floor for the benefit of the cameras, and roping in shoppers to ride alongside him, one of whom managed to fall off.

The rental bikes, he argued, had made the city safer for all cyclists, claiming London had seen a 15% increase in cycling since the scheme was launched, while overall deaths and serious injuries to cyclists had fallen.

He said: "I think we are seeing a change. Most drivers have really learned that they must expect cyclists on the roads. Maybe to begin with people found it irritating but they're getting the hang of it. They realise London is a cycle city."

The hope was that as the bikes became more common, Londoners would increasingly abandon cars for short, local journeys and errands such as shopping, he said "I'm starting to sound messianic and nannying now, but you don't need to get into a car to do some of these things."

There was no reason why the docking stations could not be extended into thus-far ignored areas of the capital, for example to the north and south-east, Johnson added: "We're prepared to go in any direction. The sole constraints are time and money."

The first phase of the rental system, which took a number of months to complete, involves a planned 6,000 machines across 400 rental points. The pre-Olympic eastward expansion will see an extra 2,000 bikes added to the fleet.

Johnson said that even as a keen cyclist with his own bike he used the scheme "from time to time".

He said: "It's a different experience, a more stately, ceremonious kind of ride It's more sit-up-and-beg, which I like. I wish my own bike was more like that – I'll have to get cowhorn handlebars."

Perhaps unfairly on Johnson's predecessor, Ken Livingstone, who first devised the scheme, the machines have become known to most Londoners as "Boris bikes". The mayor insisted he resisted this term: "I call them – religiously – the Transport for London Barclays cycle hire scheme."