Does TUPE extend to situations involving outsourcing beyond the UK?

Yes. It is well-established that TUPE can apply to transnational transfers, both within and outside the EU, as long as the transferred business is “situated immediately before the transfer in the UK” (Hollis Metal Industries Limited v GMB [2007] UKEAT/171/07 (see page 44).

TUPE can still apply even if those employed in the business ordinarily work outside the UK. For example, where there is a transfer of a UK exporting business, the fact that the sales force spends most of its working week outside the UK will not prevent TUPE applying to the transfer, as long as the business itself is situated in the UK (see BIS TUPE guidance, 2014).

https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/275252/bis-14-502-employment-rights-on-the-transfer-of-an-undertaking.pdf