Rhondda MP Chris Bryant said British journalists uncovered the scandal but US authorities were taking the lead.
Two British banks are reviewing whether corrupt payments to Fifa officials went through their branches.
Mr Bryant asked if British authorities were "lax" on tackling financial crime.
The MP has written to the prime minister asking him to call an urgent summit of British football associations, sponsors and broadcasters to agree a common approach to Fifa amid European-led calls for a boycott of the World Cup.
Sepp Blatter's re-election as Fifa president on Friday was overshadowed by the arrests on Wednesday of seven Fifa officials as part of an FBI investigation of corrupt payments.
He refused to step down despite appeals from figures including David Cameron and Michel Platini, head of European football's governing body UEFA.
Two UK banks named in FBI papers - Standard Chartered and Barclays - have launched internal reviews into whether they were used for corrupt payments by Fifa officials, the BBC understands.
But Mr Bryant told BBC Radio Wales on Monday that Mr Cameron needed to explain why UK authorities had not done more.
He said: "Some of the allegations are that it was British financial institutions that were involved in all of this, and financial institutions in British overseas territories - why on earth has there been no action in the UK?
"How many years have we known abut this for?"
Mr Bryant asked whether the British financial authorities had the resources they needed.
"So many of us are mystified why so little has been done to prosecute people in relation to Libor, in relation to banking malpractice, in relation to the economic crash and so on, and maybe we have prosecuting authorities in this country which are rather lax."
British prosecutors have been accused of failing to investigate corruption in world football by Labour's shadow culture minister, in the wake of the Fifa allegations.