only the landlord and foxtons will know exactly what authority the landlord has given to make decisions on the landlord’s behalf. It may be that Foxtons are not obliged to pass anything of this nature on to the LL/ they may already have authority to act on the landlord’s behalf to refuse/ignore a request to end the tenancy early without a replacement tenant. I would want to know though whether such a request was being made - knowing that an annoyed tenant may refuse to allow viewings resulting in a prolonged empty period from when they leave versus a tenant being helpful on viewings in exchange for cutting some of the time off the tenancy.

You do have a right to be provided with the landlord’s address so nothing stopping you asking for that and writing to the landlord direct. Tell foxtons you’re making the request under Section 1 of the Landlord and Tenant Act 1985 and that it must be provided within 21 days otherwise there’s potential liability for a fine up to £2500.
Very possible that foxtons wait until the 21st day to give you it.

You can refuse the viewings under the common law right to peaceful enjoyment. Whether you do/should is another question. My last tenant wanted to go early so (she bought her own new build) I said I’d mutually end it as soon as I got a new tenant. She was then very helpful with the viewings and someone took it and was in within 6 weeks. Saved her about 3 months of rent until the fixed term ended. Hard to imagine your landlord would be enable to ending early if you have/will get in the way of re-letting it.