Permissibility of running for MP in the UK as a Muslim

Assalaamu alaykum, In the UK, the process of becoming an official MP involves being sworn in at the house of parliament. MP-elects have to pledge an oath of allegiance to the English monarchy and parliament whilst holding a holy book of their choice. There has also been a rise in the number of Muslim candidates running for the position of MP in their respected areas with the main motivation being the genocide in Gaza and minimizing the UK's contribution I have been told by peers that pledging an oath of allegiance to a non-Muslim is blasphemous, even if its done without true convinction and just to carry out procedure. But I also believe its important for Muslims to get involved in the political environment of non-Muslim countries especially in the context of Gaza and other atrocities against Muslims said non-Muslim countries are involved in.  In light of all of this, I ask what is the permissibility of becoming an MP in the UK as a Muslim wanting to seek change for the Muslim Ummah. And based on the answer for this, what would be the general ruling for the Muslim population to take part in voting Thankyou for taking the time to read and answer my query. May Allah reward you