The &Partnership works with top brands including Cadbury, Toyota and British Gas.
Other comments in the email, which has gone viral causing mass outrage, included:
"After watching this video, I am forever flaccid."
When ranking his colleagues according to their looks, he added: "Please bear in mind that this is based solely on looks and has nothing to do with personality; if it were, there might be some right munters in there and that would defeat the whole point of trying to sexistly objectify people (on International Women's Day, of all days.)"
He signed off the email by saying: "If anyone in my Top Five(s) fancy leaving their partners and risking it all for a 'bit of mental', then my contact details are below."
Martin, whose Twitter bio describes him as a "lifelong ginger sufferer", claims the email was intended as a joke and a "stupid, ironic attempt" at mocking macho culture in the industry.
The apology, which is now pinned to the top of his profile, claims he was trying to make fun of the "Top five" emails widely regarded as a tradition at advertising agencies.
But after the email was leaked on social media, Twitter users were furious, and some branded him a "disgusting pig" and a "joke".
One woman wrote: "Good luck in the new role, Paul Martin you disgusting pig. Anyone know where his new role is (was)?"
Martin's apology reads: "On Friday 9th March, as I was due to leave my role at a London advertising agency, I sent an email around the office which had understandably offended and upset many people.
"First of all. I take full and sole responsibility for this and sincerely apologise for all offence this has caused.
"This absolutely wasn't my intention and I am incredibly sorry.
"Sending these 'Top Five' emails has become common practice at many ad agencies, and by sending that email yesterday, I have contributed to the culture of toxic masculinity.
"All the women mentioned in it are friends and people I very genuinely love and after checking with them to make sure they were happy to be mentioned in the email (as part of what I erroneously considered at the time a 'joke') I thought that was enough to validate me pressing 'send'. It wasn't and should never have been.
"The email was meant to be a stupid, ironic attempt to subvert and mock the sexist 'Top Five' emails that have been sent around agencies for many years, but I have totally missed the mark and take full responsibility.
"But saying that this was completely misjudged doesn't even begin to cover it.
"This behaviour is never something to joke about and I'm incredibly sorry for my unforgivable naivety and being further complicit in contributing to an outdated and oppressive culture for women."
A source told AdWeek that Martin only apologised after the company's joint managing director wrote an angry response to his email.
Chief executive of The &Partnership Sarah Golding has assured people "nothing like this will ever happen again".
She told Campaign: "When I received Paul's leaving email I was out of the office attending the Women of Tomorrow awards.
"I replied to him with a standard 'thank you' for your service, without reading his full message.
"Having done so subsequently, I immediately emailed the agency and then called the agency together to discuss this email, and the whole premise of leavers' emails, and have ensured nothing like this will ever happen again at The & Partnership London.
"Never have I condoned or encouraged such emails as appropriate behaviour, nor do I believe they reflect the culture of the agency.
"Most leavers messages are gentle, warm and affectionate of colleagues and time spent here, but Paul's went much further and shines a light on the dangers of a practice that no longer has a place in our agency or industry," Golding said.
