On average, the offer needs to give the jobseeker a 17 per cent pay rise to persuade them to stay.
In London, 20 per cent of movers end up in a bidding war. By contrast, only eight per cent receive counter-offers across the UK as a whole.
“As the labour market fires back into life, last-ditch tactics like counter-offers are becoming more common,” said Randstad UK boss Mark Bull.
“The result is a volatile jobs market in which the capital must work harder than ever to retain its high-flyers”.
Meanwhile the number of graduate vacancies is set to rise 11.9 per cent this year, as firms hire more new staff.
The IT and telecoms sectors are set to increase hiring of new graduates the most, according to the Association of Graduate Recruiters.