He told BBC Breakfast that second jabs offer very strong protection "but there is more protection still that we think that you can get from a booster jab and we're currently trialling which combinations of jabs are the most effective".
"When we know the results of that, then we will set out the full plans for the booster programme over the autumn," he said.
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"We've got to make sure we get the logistics right; for instance, GPs have been so heavily involved in this vaccination effort, but GPs have also got to do their day job, so that's something we're working hard on now, and, in the next few weeks, when we get the clinical data through on what's the most effective combinations to have... then we'll set out all the details of the booster programme for the autumn."
On any potential Covid-19 vaccine booster campaign, Professor Martin Marshall, chair of Royal College of GPs' Council, told BBC Radio 4's Today programme: "I do believe that general practice has a very important role to play because we were part of the successes of the current programme because general practice knows how to do it.
"But it needs to be adequately resourced to allow us to do it well.
"We can't have GPs and practice nurses and pharmacists diverted away from normal business, because we can't afford to let our patients down on all the many other things that we do in general practice."
Chris Hopson, chief executive of NHS Providers, said the health service needs time to plan for potential Covid-19 vaccine booster campaigns to make them "business as usual" instead of "emergency response".
"There are a bunch of questions that really do need to be answered in terms of looking forward to the next phase," he told Times Radio.
These include: how long protection lasts, whether people can "mix and match" the vaccines they have had, how new vaccines will be incorporated into the vaccine roster, what the level of protection is against new variants and whether vaccines need "tweaking", what the plan is for vaccinating children, and whether the vaccine can be given alongside the flu jab, he said.
Mr Hopson added: "Flu jabs start in September, so if we're going to do one jab in one arm, one jab in the other, we really do need to know quite quickly.
"And that's why we've called today for the Government to do all it can to get us the answers to those questions. We need those answers really pretty quickly if we're to carry on our fantastic success."
He added: "We've done a fantastic emergency response in terms of these vaccines up to now, but we now need to make them business as usual and we've got to basically do them alongside all the other work the NHS has got to do, which is why we're saying the more time that we can have to do that planning, the more time we've got to make this business as usual.
"To be frank, we're probably going to need to do these vaccinations, probably on an annual basis for, I don't know, at least five, six, seven, eight, nine, 10 years."