Wikipedia says:
Local elections in the United Kingdom are due to be held on 6 May 2021 for English local councils, thirteen directly elected mayors in England,[1] and 39 police and crime commissioners in England and Wales.[2] There are also elections in the parliaments and assemblies of Scotland, Wales and London, the last in conjunction with the London mayoral election.
In March 2020 the government announced that the elections scheduled for 7 May 2020 would be delayed for a year due to the COVID-19 pandemic. They are now to be held at the same time as the elections previously scheduled for 2021.[3]
The seats up for election are those last contested in 2016 and 2017. New unitary authorities to replace the county and district councils in Northamptonshire and Buckinghamshire are due to hold their inaugural elections this year.
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I'd not thought until now that this makes the elections this year a far more significant event than normal, as so many are happening on the same day.
Local issues with connections to women's rights/child safeguarding:
Schools - is your party ensuring/would your party ensure that the Dept of Education revised guidance on Relationships and Sex Education teaching has been acted on, and have you made sure that all schools are not working with organisations that tell children they can change sex, e.g. Mermaids? Links to Schoolsweek article and Transgender Trend article follow.
schoolsweek.co.uk/cancel-culture-gender-stereotypes-and-extreme-political-stances-what-new-dfe-guidance-says-about-rse/
www.transgendertrend.com/department-for-education-rse-guidance-schools/
Schools again - are you ensuring/would you ensure that toilets, changing rooms and accommodation on residential trips will remain single sex, not single gender? Link to Women's Place article on legislation showing that this is a statutory requirement for children over the age of 8.
womansplaceuk.org/mixed-sex-toilets-ins-chools/
Schools yet again! - are you ensuring/would you ensure that school staff must talk to parents/guardians if a child wants to socially transition at school and change name, pronouns etc? Would you agree that parents/guardians should never find out about this social transition after it's already happened? In what other circumstances would staff collude with a child to keep something secret from parents/guardians, in contravention of all established safeguarding principles?
Social care - are you ensuring/would you ensure that if a person who needs carers in their own home or in residential care specifies that the carers must be of a given sex, that will be biological sex, not gender? Again, basic safeguarding.
Health (relevant to Scottish and Welsh elections) - as above, in healthcare terms.
Crime - do you agree that crime statistics need to be accurate and that recording perpetrators by their gender identity instead of their biological sex is distorting that? The stats on sexual crimes are already starting to look very odd, with some rapes recorded as committed by females, when English law states that rape can only be committed if the penis is involved.
Crime again - hate crime doesn't currently include misogyny. What would your party do about that?