If the offence is committed in the UK, the nationality of the individual or organisation is irrelevant and the Act will apply.
If the acts or omissions that form part of the offence were committed overseas, they may still be prosecuted if committed by British nationals, a national of a British overseas territory or UK corporate organisations.
The law also covers foreign nationals "ordinarily resident" in the UK. They may be liable for such offences, even if they are committed abroad.
A UK company is not liable under the above offences if the bribe is committed abroad by its foreign subsidiary. The foreign subsidiary is also not liable in that situation. The position may be different, however, in relation to the corporate offence under section 7.
A corporate body can be held to have committed any of the above offences. If the offence committed by a corporate body was proved to have been committed with the "consent or connivance" of a senior officer, both the officer and the corporate body will be guilty and liable to be prosecuted for the same bribery offences. One party is not somehow guilty of a "lesser offence". Alternatively, the senior officer may be liable directly for any of the above offences.
The provisions apply to both the public and private sectors.