Asking a question in the House of Lords, Bishop Paul Butler said the omicron variant showed that the virus "knows no national boundaries."
He said: "In the light of the new omicron variant that has dominated the news over the weekend, my colleague Archbishop Thabo Makgoba of Cape Town urged those of us in rich countries to do better at narrowing inequality of vaccination rates, which are 7% in Africa and 70% in Europe.
"We must acknowledge that this virus knows no national boundaries and will spread, mutate and return to us in the way that we are seeing, so we need a global approach, not simply a bilateral approach.
"Will Her Majesty’s Government’s commit to redoubling efforts to seek a truly global approach to vaccine donation to ensure that people in all nations are safer?"
Lord Goldsmith of Richmond Park, on behalf of the Government, replied: "My Lords, the Government strongly agree and we are committed to supporting rapid, equitable access to safe and effective vaccines through multilateral co-operation to end the acute phase of this pandemic.
"That is why the UK supports the COVAX facility and was one of the first countries to do so. It is, as the right reverend Prelate knows, a multilateral mechanism that supports access by pooling resources to accelerate the development, manufacture and delivery of vaccines.
"More than 537 million vaccines have so far been delivered globally through that scheme."