Downing Street has said the football authorities need to do more to tackle racism in the game after calls for a government inquiry and more comprehensive sanctions in response to alleged racist incidents during a match between Tottenham Hotspur and Chelsea on Sunday.

Boris Johnson’s spokesman said the government was monitoring the authorities’ response and was ready to take further steps “if required”.

“Racism of any kind has no place in football or anywhere else and we must confront this vile behaviour,” he said. “Clearly there remains more work to be done by the football authorities in tackling this issue and we are committed to working with them on this to stamp it out.

The spokesman added: “The FA, Premier League and English Football League have significantly stepped up their efforts, but we expect them to continue to prioritise this issue and to consult with both players and supporter groups, and we will be monitoring how the football authorities implement their plans through the season.”

No 10’s comments were echoed by Priti Patel, the home secretary, who said: “Those found guilty of a racially aggravated offence under the Public Order Act can face a sentence of both six months in prison and a 10-year ban from attending all football matches.

“We fully expect the entire football community to work with the authorities to bring the perpetrators to justice so we can stamp this evil out of our national game.”

Earlier, the Professional Footballers’ Association (PFA) said: “Once again, a Premier League fixture has been tainted by abuse from the stands towards players. We believe that the time has come for all governing bodies to unite collectively to end this abuse.

“The PFA calls for a government inquiry into racism and the rise in hate crime within football, and immediate and urgent action from an all-party group at the Department of Culture, Media and Sport to address this urgent issue.”

It was reported that the sports minister, Nigel Adams, would speak to Tottenham Hotspur about the abuse on Monday.

The game on Sunday was paused after the Chelsea defender Antonio Rüdiger was allegedly targeted with racist abuse by a section of the crowd.

The referee Anthony Taylor stopped the game during the second half when an object was thrown at Chelsea’s goalkeeper, Kepa Arrizabalaga, and Rüdiger indicated that a supporter had shouted a monkey chant at him.

César Azipilicueta, the Chelsea captain, brought the incident to the referee’s attention, who asked for an announcement to be broadcast to the crowd. The announcement over the PA system at the Tottenham Hotspur Stadium told the crowd that “racist behaviour is interfering with the game”. It was repeated twice, though it is understood that only one allegation of racism was made.

On Monday, it emerged that a Chelsea supporter was arrested for racially abusing Tottenham Hotspur’s Son Heung-min during the same Premier League match.

It came as Spurs earlier vowed to take the “strongest possible action” against anyone found guilty of abusing Rüdiger, who is understood to have been left angry following the latest example of the racism blighting the game. The alleged abuse occurred shortly after Rüdiger was involved in the incident that led to Son being sent off.

Damian Collins MP, who chaired parliament’s culture, media and sport committee, said players must be made aware of their right to walk off the pitch if they face racist abuse. He said: “I think players [should be made] well aware of what their rights are – that if they’re unhappy with the behaviour of people in the crowd and unhappy that behaviour has not been stopped, that if they choose to come off then they will be backed up by the football authorities in doing so.”

The incident at the Tottenham ground was the latest of several racist incidents to mar English football over the past 12 months. The Manchester derby sparked a furore after a City fan appeared to make a monkey gesture at United’s player Fred, while on the same day a League Two game between Scunthorpe and Forest Green Rovers was halted after allegations of racist abuse. In October an FA Cup tie between Haringey Borough and Yeovil was replayed after racist abuse from the crowd.

Kick It Out’s George Starkey-Midha echoed the PFA’s call for the government to take action. He told BBC Radio 4’s Today programme: “It’s imperative on everyone involved in football, on the government, or anyone in any kind of position of authority, to begin to take this far more seriously and look at how we can begin to make inroads, because clearly you’ve now got a situation where every single week there seems to be another incident and it’s a serious, serious problem.”

Starkey-Midha said there needed to be “far more robust” reporting procedures and “far more comprehensive sanctions”, including within football, to respond to racism. When asked if the PFA was accurate when warning of the “blatant racism that is currently rife in the UK”, Starkey-Midha replied: “Yes, absolutely. I think it’s undeniable that racism is still a very serious problem in this country.”

He added: ““I think people like to look abroad to Italy, Russia and Bulgaria when incidents happen there and I think we’re right to criticise when we see it, but there are serious levels of racism in this country still too. Unless we wake up to that fact, we won’t tackle it properly.”

The former cabinet minister David Mellor called for fans to do more to root out racism at football matches in Britain. Mellor told PA Media: “Fans cannot escape responsibility for clearing racism out of the game. Somebody must know who this idiot or these idiots are.

“Fans cannot just pass by on the other side of the road, they must stand up and be counted otherwise we will be on a slippery slope and it will lead to matches being abandoned, stadiums being closed and games being played behind closed doors.”

Mellor, who presented BBC radio’s 606 football phone-in programme for nine years, added: “What we cannot do is take issue with racism when British teams play in eastern Europe and then ignore incidents over here. Fans cannot be morally neutral about this.”