According to UK Ministry of Defense official answer to a parliamentary request about flights that carry nuclear materials, the United Kingdom and the United States regularly transfer weapon-related material between the two states:
In the last five years, 23 flights carrying Defence Nuclear Materials (DNM) were undertaken. All flights were between the UK and the United States on fixed wing aircraft under the control of UK Armed Forces.
The MoD answer, however, withheld "details of the physical state, mass and radiological quantity of DNM transported."
The material in question is most likely highly-enriched uranium, which the United States supply to the United Kingdom under the 1958 Mutual Defense Agreement, which has been regularly amended and extended (most recently in 2014, extending it to 2024 and modifying some provisions). According to the U.S. administration, the agreement permits "the transfer between the United States and the United Kingdom of classified information concerning atomic weapons; nuclear technology and controlled nuclear information; material and equipment for the development of defense plans; training of personnel; evaluation of potential enemy capability; development of delivery systems; and the research, development, and design of military reactors."
Transfers of the special nuclear material appear to be a routine practice. According to the U.K. Campaign for Nuclear Disarmament, "between 1 January 1993 and 22 August 1999 there have been 15 flights into Britain and 32 flights out of Britain to the United States."
IPFM estimated that the United Kingdom received at least 14 tons of HEU from the United States in 1958-1993 (see Global Fissile Material Report 2010, pp. 72-73 for details). Apparently, the transfers continued after that. The two countries also exchanged some plutonium as well (GFMR10, p. 78)