Priti Patel's plan to use First past the post (FPTP) rather than supplementary vote probably won't give them much, if any advantage, and actually may hurt their cause of getting more Tories in office.
See the report at: https://www.theguardian.com/politics/2021/may/09/government-to-change-english-voting-system-after-labour-mayoral-victories
It's seductive for the Conservatives to look at the London Mayor election and see how an FPTP lead by Khan over Bailey was doubled when it came to counting the second preferences, and a light switches on in their heads and they think, let's make it FPTP!
But things don't work quite that way. Of course us greens would like to think that a vote for the Green Party will always be a vote for the Green Party come rain or shine, but in reality it isn't. If people sense that their Green vote could end up letting in a Conservative by default then a lot, if not most, of the London green voters are likely to peel off and vote Labour in a FPTP contest. Result - Bailey loses by much the same margin as he has done. Moreover if the seat allocation for the London Assembly itself is decided by FPTP then there will be a straight Labour majority rather than the current 'hung' position - not much help for a Tory Mayor there either!
In general the sometimes-talked-about disintegration of the non-Tory vote (which weakens Labour) could actually be staunched if the Government purges the current electoral arrangements in the cities and sets up straight FPTP elections. It's called unintended consequences. There's a lot of it about!