That's not strictly true, what the UK did, together with most western countries including the US & EU block, was to vote to protect patents, had we voted against it, it would have made different to the outcome.
What we went on to do is contribute millions to the COVAX fund, and as
Sunray has just pointed out, came to an agreement with AZ to sell at cost price to ensure the maximum number of doses can be delivered to poorer countries. The AZ vaccine is being manufactured all over the world, so poorer countries will be getting it from various supply lines fairly quickly, with the UK factories contributing more supplies in time.
Sadly, we can't vaccinate the whole world within a few months, but the UK has been a leader in ensuring poorer countries get it as soon as possible.