Statistics gathered by the anti-discrimination charity showed reports of racism in English football rose by 43% – from 192 to 274 – last season.
“I think you can’t not link them together,” Wood told BBC Sport.
“We’re seeing a lot of reports of ‘go back to where you came from’ which we haven’t seen for a while which seems to be on the back of Brexit.”
Factoring in all forms of discrimination, reports of abuse in professional and grassroots football increased by 32% to 422, up from 319 during 2017-18. A further 159 reports were received via social media.
Reports of faith-based discrimination – including Islamophobia and anti-Semitism – rose by 75% from 36 to 63, a higher percentage than any other form of abuse during the period.
It is the seventh consecutive year reported incidents of discrimination within football have increased, and the 581 total reports is more than double the figure from five years ago.
“If we’re seeing a rise in hate crime, the Home Office is seeing a rise in hate crime and other bodies are seeing a rise in hate crime, it’s linked because that’s what is going on in society at the moment. If it’s there, we’ll see it in football,” Wood added.
“In some of the cases we have seen, there is a real hatred there which we haven’t maybe seen as much of in the past where it’s really violent and very targeted, particularly on social media.
“Some of the social media reports we’ve seen you wouldn’t want anyone to see.
“We’re talking to people all the time that feel, post-Brexit, that ‘maybe this country isn’t for me’.
“[Politicians] have to take that responsibility very seriously, they are the leaders of the country and they need to set the tone. Society is reflected in football.”