The U.S. oath is very similar to the UK one. Not so the oath currently being proposed. The oath under proposal requires non-Jewish applicants for citizenship to affirm loyalty to Israel as a Jewish and democratic state. Although you Brits do have a national church, I don't believe there is anything in your citizenship oath or in any oath of office requiring anyone to swear loyalty to the Church of England (at least not in the last 150 years or so).
Defense Ministry says had no knowledge of alleged improper defense deals by Gal Hirsch (Haaretz)
from the article: Loyalty oath is not about Arabs, it’s about hatred of liberal values