Pensions & Investment Research Consultants (Pirc) has advised shareholders not to roll over on the remuneration report at the baker's AGM on Tuesday.
While the group acknowledged that the increase in chief executive Roger Whiteside's salary was reflected in compensation packages across the rest of the company, it called the 79:1 chief executive pay ratio "not appropriate" and slammed the variable pay award element of the total paypacket as "excessive".
Whiteside stands to take away £2.6m in total for his performance in 2015, a significant spike from £1.2m the year before, although the increase is mainly caused by £1.4m worth of long-term incentives vesting in the more recent year.
Greggs is yet to respond to City A.M.'s request for comment.
Meanwhile, the Mail on Sunday reported this weekend that Pirc had also taken issue with the executive pay at Lloyds Bank and broadcaster ITV, advising a vote against the remuneration report at the former and to abstain on remuneration at the latter.
According to the companies' annual reports, Lloyds group chief executive Antonio Horta-Osorio will recieve £8.8m for 2015, down from £11.5m the year before, while ITV chief executive Adam Crozier stands to get just shy of £4m, down from £4.8m in 2014.
Both Pirc and ITV are yet to respond to City A.M.'s request for comment, while Lloyds declined.
Shareholders have been noticeably heated in their approach to executive pay this AGM season, with remuneration resolutions passing with the narrowest of margins at Man Group and Anglo American, while shareholders at BP refused to pass the resolution on chief executive Bob Dudley's near $20m (£14m) paypacket.
However, other meetings have been more chilled, with resolutions passing with relative ease at the likes of Rolls Royce and GlaxoSmithKline.