Across Britain, it now takes 63 days for such properties to find a buyer, compared with 81 days a year ago, according to Rightmove.
Rightmove said the hottest millionaire markets are currently in the counties of Norfolk, Wiltshire and Cornwall.
At a more local level, Rightmove said million-pound property markets are moving particularly quickly in Hackney, Tooting, Stoke Newington and Balham in London, as well as in Cambridge and the town of Berkhamsted in Hertfordshire.
Rightmove’s director of property data, Tim Bannister, said: “Houses in the million-pound-plus market have always taken longer to find buyers than the wider market because of their higher price points, but our new analysis shows that wealthier buyers who are fortunate enough to be able to move to bigger homes have been driving this sector of the market to a pace not seen since back in 2014.
“Unsurprisingly, the counties seeing the biggest annual rise for sales agreed of million-pound homes all benefit from beautiful coasts and countryside.
“Available stock in this price bracket is up around 2% compared to this time last year, which is the first time since 2018 that there’s been an annual jump, meaning there’s a little bit more choice for this group of buyers.”
Lucian Cook, head of residential research at Savills, said: “The amount of housing wealth at their disposal and relative security of their household finances mean £1 million-plus buyers have been quick to act on their changing housing needs and priorities.
“Driven by a re-assessment of their work-life balance, desire for more space and the expectation that they will work from home more often, they’ve led the surge in agreed sales seen since the market reopened.
“This has fed demand for good quality family homes along London’s established wealth corridors and, more noticeably, in towns such as Guildford, Winchester and St Albans, villages within striking distance of a mainline station and lifestyle relocation markets such as Devon, Suffolk and North Yorkshire.”
Tom Bill, head of UK residential research at Knight Frank, added: “Demand in higher price brackets is more responsive to external events and we saw the same after the global financial crisis.
“Buyers who are less constrained by the mortgage market and negative sentiment around unemployment and the economy have been able to act on their desire for more space.”
Here are the top 10 counties with an annual percentage increase in sales of homes priced at £1 million-plus, according to Rightmove:
1. Norfolk, 244%
2. Wiltshire, 174%
3. Cornwall, 165%
4. Gloucestershire, 153%
5. Berkshire, 134%
6. Dorset, 131%
7. West Sussex, 120%
8. Somerset, 117%
9. East Sussex, 107%
10. Suffolk, 105%