The sudden departures follow last month’s profit warning, which wiped nearly a third off Connaught’s share price.
“Mark Tincknell has agreed with the chairman that in order to recover from health issues he will relinquish his role as chief executive with immediate effect,” said a company statement.
Tincknell, who has been at Connaught for 28 years, will continue to have an on-going role with the business and will help in the search for his replacement.
The firm also added that Stephen Hill finance director had also decided to quit in October.
Connaught added: “The Board respects his decision and he leaves with their thanks for his contribution over the last four years.”
Three weeks ago, Connaught warned that Government spending cuts will severely hit revenues and profits at its big social housing arm.
The profit warning saw Connaught’s share price plunge by a third and sent shivers through the sector.
Since then rival social housing contractors like Mears, Morgan Sindall and Kier have failed to see dramatic cuts in their work programmes.
Connaught said it had identified 31 social housing contracts where a proportion of work had been deferred.
It estimated over the next two years this would knock expected revenue by around £200m and depress forecast profits by £29m.
At the half year results, published in February, Connaught group sales stood at £355m.
At that time chief executive Mark Tincknell said Connaught would be exiting underperforming areas as contracts expire.
Then he warned revenues in social housing were expected to fall by £25m in 2010 and £40m in 2011.
Connaught expects a one-off impact to its cash conversion rate, reducing to around 40% this financial year.
In today’s statement, the board said that it would continue to monitor cash levels against covenant compliance with vigilance, though based on current expectations it fully expected to be able to operate within existing covenant levels.
The firm said it would also continue with a cost reduction programme that is expected to save at least £25m for financial year 2012.
Chairman Sir Roy Gardner said: “The outlook for Connaught remains positive. The cost reduction programme will realise significant savings whilst providing a solid platform from which we can achieve further growth.
“Our order book is strong and our newly-formed big ticket sales team will ensure we capitalise upon a record pipeline of enquiries.
He added: “I believe the group is ideally placed to meet the needs of our clients which in these uncertain times are focused upon achieving budget savings while maintaining a high level of customer service.”
Connaught also maintained that the medium-term outlook for the business remained strong with the revised order book at £2.6bn and pipeline work a record £5.3bn