Not by using the law as currently written.
In the UK, MPs are elected to parliament as individuals, not as members of a political party (although the party they are standing for can be named on the ballot paper if the individual chooses). As such, once duly elected, an MP will only lose their seat if:
- They choose to take certain (meaningless) offices of profit under the Crown. This is used as a method of resigning without actually resigning, and needs the consent of the individual in question.
- The MP is sentenced to prison for a period greater than one year.
- The MP is sentence to prison for a period of a year or less, is suspended from the House of least 10 sitting days or 14 calendar days, following a report by the Committee on Standards or receives a conviction for providing false or misleading expenses claims and a petition is collected containing signatures of more than 10% of the voters in their constituency, under the Recall of MPs Act 2015.
- The MP dies.
While a party could try placing moral pressure on an MP to give up their seat having lost the whip, none of the options allow for direct party input.