Four officers were injured when the Met's Flying Squad swooped on the men in Piccadilly at 11:25 BST.
A Taser was discharged several times and the policemen were hurt as the men tried to escape on mopeds.
Four men have been arrested and are being held at London police stations.
A Met Police spokesman said three officers suffered minor injuries and the fourth is in hospital in a serious condition.
Store owner Avi Reed said the gang smashed a glass cabinet, causing more than Â£300,000 of damage,
Mr Reed said police contacted them at the Chronext store earlier to warn them that there might be a robbery, and the shop was closed to protect customers.
He said: "At about 11:30 we saw three guys, they had helmets on. One tried to smash the door with a hammer. The glass didn't break as it's protected but he managed to get in.
"Another guy had an axe and managed to smash a cabinet, while the other stayed on the motorbike. They caused enormous damage."
Mr Reed praised the actions of the "amazing" police.
Det Supt Craig Turner, said: "Our officers are absolutely committed to keeping London safe and target the criminals who pose a danger to Londoners and our city businesses day in, day out.
"They know that this work carries with it very real risks and dangers but take this in their stride as part of serving the public.
"However, today's events highlight how the reckless behaviour of those determined to evade justice, heedless of the consequences, can have a real impact on all those involved."
Piccadilly was closed eastbound at Hyde Park Corner for about six hours while investigations were carried out.

The African champions let in goals from Kerem Demirbay and Timo Werner, who netted twice, while Vincent Aboubakar grabbed a consolation goal for them.
The Indomitable Lions also had Ernest Mabouka sent off after confusion involving the Video Assistant Referee.
Sebastien Siani was initially dismissed in a case of mistaken identity before the error was corrected.
Colombian referee Wilmar Roldan consulted the VAR after a high challenge by Mabouka on Germany's Emre Can led to Cameroon captain Siani wrongfully receiving a yellow card.
However, the initial outcome was to switch the colour of Siani's card to red.
It was only after Cameroon's players insisted he review the incident again that he realised his error, rescinded Siani's dismissal and sending off the correct culprit Mabouka.
"The referee didn't give any explanation," said Cameroon coach Hugo Broos.
"First of all he gave a red card against Siani, then the video ref called him back and told him it was the wrong player, so Mabouka was sent off.
"Both players [Can and Mabouka] had their legs high, so I don't see why he had to give a red card. I think everyone is confused
"I didn't understand it and I still don't understand it now.
"I think this is something for the referee. He and he alone can explain what happened in that incident."
As Group B winners, Germany will face Mexico in the last four in Sochi, Russia.
Portugal will play Chile in the other semi-final.
A moped gang armed with knives and an axe has been intercepted by police in a "terrifying" attempt to rob a luxury watch store in central London.
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Cameroon's Confederations Cup campaign is over after a 3-1 defeat by Germany in their final Group B game on Sunday.