The BNP will inevitably face a series of legal challenges on issues ranging from discrimination and employment law to possible criminal offences, lawyers say, following two candidates' election to the European parliament.

The party's constitution, which says membership is "strictly defined within the terms of … 'indigenous Caucasian' and defined ethnic groups emanating from that Race" is a breach of the law against discriminating in membership organisations, according to legal experts.

"An unincorporated association like the BNP which has genuine screening for membership cannot unlawfully discriminate," said Gavin Millar QC, who specialises in election and discrimination law. "There will inevitably now be legal challenges to this.

"It was presumed before that the BNP were so unimportant that it wasn't worth trying, but now this is a live issue, and the BNP's constitution must be challenged."

Possible challenges to the constitution could make use of a Lords ruling which found that political parties could be regarded as "members' clubs" and therefore fell within discrimination law.

Lawyers also said that as the BNP gets access to the European parliament, with a budget for employing staff and contracting services, it would also be open to employment law, which prohibits direct and indirect discrimination.

"A black or Jewish candidate who applied and didn't get the job on grounds of their racial or religious background would have a claim in the employment tribunal," Millar said.

"If an individual challenges and they maintain a practice not employing any visible minority people, there is no doubt that like any employer who has such practices, they can be sued," said employment barrister and chair of the Society of Black Lawyers, Peter Herbert. "When they are in receipt of public funds they will have to be an equal opportunities employer. To do otherwise would be incompatible with public office.

"I can see the equality commission mounting an inquiry into how the BNP operate now. The office of public standards could also inquire."

The questions came as BNP leader Nick Griffin was pelted with eggs at an event in Manchester. Griffin picked up a seat in the north-west of England and Andrew Brons won a seat in Yorkshire and the Humber, a breakthrough in national elections for the far-right party.

Labour MEP for London Claude Moraes, speaking at a Unite Against Fascism press conference in Westminster, said: "There is real damage here to Britain because we have never elected fascists in a national election. Fascists in the European parliament have long wanted members from Britain to join this transnational group.

"There was a long period in which we could have said neofascists would not be elected in Britain to represent us in an international parliament."

In addition to the BNP's membership and employment practices, lawyers said that policies once supported by the BNP but now abandoned by its official representatives – including non-voluntary repatriation and forced sterilisation of non-white women – may attract criminal liability for some BNP activists.

Said Millar: "One of the stresses for Nick Griffin is constantly having to say to the membership that this is no longer a policy they can espouse in public. It is a constant source of tension within the party."

Criminal lawyers said there was no doubt that members who espoused those policies could be liable for charges of inciting racial or religious hatred. "Any policy which incites racial hatred will be liable," Herbert said. "Twelve years after Stephen Lawrence this is a sad place to be."

A number of BNP members already have criminal convictions for race-related offences, including Griffin, who was given a two-year suspended sentence for incitement to racial hatred after publishing material denying the Holocaust in 1998.

Although in 2006 Griffin and party activist Mark Collett were cleared of race hate charges relating to speeches he made describing Islam as a "wicked, vicious faith", Griffin last month told BNP members in an online broadcast that he had no problem with breaking race laws.

"As you know, we don't break the law. We never have, we never will, you know, on financial things. Don't mind breaking the odd race law, or being accused of it, you know, inadvertently," he said.

But lawyers said criminal convictions were difficult to obtain in practice, with an average of only three successful prosecutions per year for inciting racial hatred.

"[BNP activity] will only be criminal if … the material is threatening, abusive or insulting, and also it must be intended to stir up racial hatred," said Kirsty Brimelow, a barrister who specialises in racial and religious hate crimes. "If BNP leaflets contain extreme racism, there will be a case that they are trying to undermine public order and the rights of the targeted minority – [so] they would not be able to rely on their right to free speech."