Underlying tax is the term used to refer to foreign tax already suffered by a foreign company on profits out of which a dividend is paid to a UK investor. In certain circumstances, relief for underlying tax is given to investors in foreign companies, either under the relevant double tax treaty or under the Taxation (International and Other Provisions) Act 2010 (TIOPA 2010), ss 9, 12, 14-16.
Relief is generally only given for these purposes to a company with at least 10% of the voting power in the underlying company (whether direct or indirect).
Underlying tax is only relevant to dividend payments. No similar concept applies for the purposes of partnership distributions and so the classification of the foreign entity and the distribution made is vitally important (see the Memec (Memec plc v IRC  STC 754) and Anson (Anson v HMRC (aka Swift v HMRC)  UKSC 44) cases).
Note that underlying tax is different to a withholding for foreign tax on the dividend itself.
HMRC guidance can be found at INTM164060, INTM164360, INTM167370 and INTM167410.