I am sure they are not interested in Rishi who will be out of Nr 10 in a month!
I doubt they are interested in him personally unless he was a particular friend.
Perhaps - since, according to you, they would need/want to invite the PM to curry favour - they should have just sent an invite to:
To Whom it May Concern
10, Downing Street
Tbh, I don't think they need to invite people they don't know to attempt to advance their interests.
Sounds like it was a wedding with primarily friends and family on both sides invited.