By Nick Eardley
BBC political correspondent
The Liberal Democrats are trying to force ministers to hold the Mid Bedfordshire by-election at the start of October.
Nadine Dorries resigned as an MP there last week.
The government has not confirmed when it will formally start the process to hold a by-election.
The Lib Dems have said they will break convention and table a motion themselves if the government does not, on Monday when Parliament returns.
That would mean the election to succeed Ms Dorries could be held on 5 October – the day after the Conservative conference finishes and the earliest possible date.
The Lib Dems said they wanted to minimise the amount of time that the area is without an MP.
Under parliamentary convention, the party of the departing MP normally starts the formal process for a by-election. It usually takes six or seven weeks from then to polling day. But there is nothing to stop others tabling a motion, which MPs could then vote on.
The Conservatives have a majority in Parliament and could therefore block any motion, but that would lead to accusations they are delaying the by-election.
The race in Mid-Bedforshire will be a key test of support for the main political parties. The seat has been held by the Conservatives since the 1920s but both Labour and the Liberal Democrats are throwing resources at the seat to try and win it.
It’s possible however that could split the anti-government vote.
Liberal Democrat deputy leader Daisy Cooper said: “People in Mid Bedfordshire have been denied a voice in Parliament for far too long, all because Nadine Dorries abandoned them and Rishi Sunak refused to do anything about it.
“They should not be made to wait a day longer to elect an MP who will finally stand up for them.
“It would add insult to injury if Rishi Sunak now decides to delay this by-election for his own political reasons.”
A government spokeswoman said: “The PM has been clear that the people of Mid Beds deserve proper representation. A by-election will take place in a timely manner.”
There will be another key by-election in early October in the Rutherglen and Hamilton West seat in Scotland, previously held by Margaret Ferrier.
That seat will be a key test of the political mood in Scotland. Labour see it as crucial to show evidence they are capable of staging a significant comeback in Scotland. It will also be a first big electoral test for the new SNP leader Humza Yousaf.
The SNP has said it will move the writ for that vote on Monday – meaning it will be held on 5 or 12 October.