Police are investigating a funeral attended by "between 400 to 500 people", despite government guidance stating only 30 mourners are allowed.
Bedfordshire Police dispatched officers to the area when "large crowds" gathered outside a church in Dunstable.
Conservative MP for the town Andrew Selous said he was very angry about the "flagrant breach" of rules at the "traveller funeral".
The force said it will review evidence and consider taking action.
Ch Insp Lee Haines said: "We worked with the local authority, the cemetery and the funeral directors prior to this event so people could attend to pay their respects while following social distancing measures.
"The funeral was initially attended by lower numbers of people, as planned, but larger crowds subsequently started gathering outside the church where the funeral was taking place."
Mr Selous, the MP for South West Bedfordshire, said the number of people attending the funeral at St Mary's Church in West Street was "completely unacceptable".
"Bedfordshire Police tell me they estimate that there were between 400 to 500 people present when only 30 are allowed at a funeral," he said.
"We are all under the law and it is simply not right or acceptable for the rest of the population who have made such sacrifices to see others getting away with such behaviour."
Bedfordshire Police said officers "understand that people wish to pay their respects to their loved ones... but everyone needs to follow the rules".