I am a trustee at our local Methodist Church. The Methodist Church is slightly unusual as although the UK body is a charity many local churches don't have their own charity number but function as one via the national body.
It is rather off-topic, but that was never the case.
The large national charity I mentioned further up the thread was the Methodist Church; I served on Conference for ten years, so was a trustee of the national charity until much more appropriate arrangements were put into place, with the trustee body for the national charity now being the Connexional Council.
Historically, most of the local churches were exempt charities and did not have to register with the Charity Commission, but for legal purposes they were distinct from the national charity. Subsequent changes in the law have meant that essentially all local structures have had to register as charities; in many areas, this goes down to the local church level, but there are exceptions. The national custodian trustee, the Trustees for Methodist Church Purposes, holds land and buildings on behalf of the local managing trustees, and various functions are provided nationally by the Methodist Church or TMCP. The Methodist Church Act 1976 sets out the overarching legal principles and implements the provisions in the Deed of Union and the Model Trusts.
We have had a Vodafone broadband dongle under contract for some years and will be moving to their FTTP package next month via City Fibre (a long story, but it has taken them three years to sort out a post code address issue..). At no time have they ever queried whether we are a charity or business and have never demanded a charity number. We do seem to be completely on the domestic charges.
A lot will depend on how the infrastructure provider (Openreach, CityFibre, etc.) classifies the building they are serving. I think most churches are more likely to be classified as business premises, so you will likely deal with the SME (small and medium enterprises) team at an ISP, though this is not a universal rule.
There are a few charity-specific deals around, but there is no compulsion for an ISP to offer special rates to charities, and most seem not to.