Hate crimes against Muslims have soared in the UK this year, figures show.

Hundreds of anti-Muslim offences were carried out across the country in 2013, with Britain's biggest force, the Metropolitan police, recording 500 Islamophobic crimes.

Many forces reported a surge in the number of anti-Muslim hate crimes after the murder of soldier Lee Rigby by two Islamic extremists in Woolwich, south-east London, in May.

But the figures could be much higher as nearly half of the 43 forces in England and Wales did not reveal how many hate crimes had targeted Muslims. Some forces admitted they did not always record the faith of a religious hate-crime victim.

Freedom of Information requests were sent by the Press Association to every police force in England and Wales. Of the 43 forces, 24 provided figures on the number of anti-Muslim crimes and incidents recorded.

Tell Mama, a group which monitors anti-Muslim incidents, said it had dealt with 840 cases since April, with the number expected to rise to more than 1,000 by the end of March. This compared with 582 anti-Muslim cases it dealt with from March 2012 to March 2013.

Fiyaz Mujhal, director of Faith Matters, which runs the Tell Mama project, said the reaction to the murder of Rigby had caused the number of Islamophobic crimes to jump significantly.

"The far right groups, particularly the EDL [English Defence League], perniciously use the internet and social media to promote vast amounts of online hate," he said.

Mujhal said tougher sentencing was needed to tackle Islamophobic crime and that guidelines by the Crown Prosecution Service (CPS) to monitor social media were not fit for purpose.

"They raised the bar of prosecution significantly. Now, unless there is a direct threat to somebody on Twitter or Facebook, the CPS will not prosecute. The CPS is just plainly out of sync with reality.

"We also need more robust sentencing. In one case, a pig's head was left outside a mosque and the perpetrator came away with a community sentence. When you target a mosque, you are targeting the whole community."

Tell Mama has called for police forces to improve monitoring of Islamophobic crimes.

"There are three problems we come across," Mujhal said. "Firstly, there is a lack of understanding of the language of Islamophobia thrown at victims in any incidents. Secondly, there is very little training on how to ask relevant questions to pull out anti-Muslim cases.

"Thirdly, recording processes are not in line with each other. One force will allow an officer to flag an incident as anti-Muslim, another force will flag it as religious hate crime. There is no uniformity.

"There must be guidelines for all forces so we can know the level of the problem."

A CPS spokeswoman said: "Online communication can be offensive, shocking or in bad taste.

"However, as set out in CPS guidelines on prosecuting cases involving communications sent via social media, content has to be more than simply offensive to be contrary to the criminal law.

"In order to preserve the right to free speech the threshold for prosecution must be high and only communications that are grossly offensive, indecent, obscene or false are prohibited by the legislation."

The Association of Chief Police Officers (Acpo) has previously said 71 incidents were reported to its national community tension team over five days after Rigby's murder on 22 May.

Superintendent Paul Giannasi, Acpo's spokesman on hate crime, said: "The police service is committed to reducing the harm caused by hate crime and it is vital that we encourage more victims who suffer crimes to report them to the police or through third party reporting facilities such as Tell Mama.

"Acpo has played a key role in improving reporting mechanisms, including through the development of our True Vision website. This provides information to victims and allows people to report online.

"We would obviously want overall crime levels to reduce and to see fewer victims, but we welcome increases in reported hate crime, as long as they are a sign of increased confidence of victims to report.

"We are working with local police forces, to help improve the way we respond to hate crime and to provide robust and transparent hate crime data."

A justice ministry spokesman said: "These are despicable crimes that devastate lives and communities.

"The courts already hand out tougher punishments where race or religion are found to be aggravating factors. The number of people receiving a custodial sentence for these appalling crimes is higher than ever before."