In some cases yes, held the Court of Appeal in Benkharbouche and Janah v Sudan and Libya.
The Appellants worked as service staff in the Sudanese and Libyan embassies in London. Between them, they brought claims for unfair dismissal, arrears of pay, race discrimination, harassment and claims in relation to the national minimum wage and Working Time Regulations 1998.
The Court of Appeal held that the blanket immunity from claims provided by section 16(1)(a) of the State Immunity Act 1978 went beyond the UK's obligations in public international law. ApplyingHolland v Lampen Wolfe  1 WLR 1573, if section 16(1)(a) had been a mere implementation of international law obligations, there could have been no question of a violation of Article 6 of the Human Rights Act 1998.
The Court examined a number of treaties to which the UK is party and customary international law, and concluded that a blanket ban was not required in international law and did not fall within any margin of appreciation. It was not a proportionate means of achieving a legitimate aim: attempts in the case law to justify similar bans related to the legitimate aim of implementing international law obligations. Section 16(1)(a) is therefore incompatible with the Human Rights Act. The remedy was a declaration of incompatibility.
The Court of Appeal came to the same conclusion on SIA section 4(2)(b) which bars claims where the claimant is not habitually resident in the UK.
The Court of Appeal agreed with Langstaff P in the EAT that the immunity also violated Article 47 of the EU Charter ("Everyone whose rights and freedoms guaranteed by the law of the Union are violated has the right to an effective remedy before a tribunal") which, enshrining a general principle of EU law, was directly effective against the Respondents. The Appellants could therefore proceed in their claims "guaranteed by the law of the Union": claims under the WTR 1998, and claims for racial discrimination and harassment.