The US paid for all the expenses for the Sth Korean Corps of 2 Army divisions and a Marine Brigade and the Thai Army division to fight in the Vietnam War. These were infantry heavy forces, with their own artillery but no armour, helicopters, attack aircraft, warship, air and sea transport.
In contrast Australia and New Zealand paid for everything involved in their deployments from meals and accommodation in transit messes to shells expended by US artillery units and bombs/fuel by US aviation units expended in support of Aus/ANZAC units. In addition the Aus/NZ was a very differnet contribution, the core of the force was an infantry Brigade group but this had its own organic Tanks/APC directly supported by RAAF/Army helicopters, the RAAF deployed a bomber squadron, the RAN a destroyer supported entirely by RAAF/RAN air/sea lift and charted civilian support as well.
I assume requests for a British contribution to Vietnam were based on the Aus/NZ model of a balanced forces fully paid for by Britain.
But WI the US offered to pay for a British contribution to Vietnam like the SthK and Thai deployments? Firstly, would Britain actually send a force to Vietnam if the US was paying? Secondly, what would Britain send if the US was paying; a smallish but balanced Army force backed by decent RN and RAF forces like the Aus/NZ or a large infantry heavy force relying on US combat support? Thirdly, how would this affect the Aus/NZ contribution; would they form a Commonwealth Division/Wing/Task Force, would Aus/NZ get a financial break?