I checked several companies online in advance, as it was so easy to do online.
We went with Sky - no problems at all, no "credit" required. Once I signed up (using my credit card) and then switched to direct debit (everything seems to want you to pay direct debit over here) there have been no issues at all.
I was also told by a few places I couldn't get a cell phone without having been here for several months ("no credit") so I have a pay-as-you-go from EE; but, when speaking with them last week, was told I was eligible for a sim-only plan (not pay-as-you-go) that was only slightly more expensive than the PAYG plan, but since we rarely use the phone I didn't see a reason to sign up for it. SO, the "no credit" thing doesn't seem to be a hard-and-fast rule for cell phones, either.
You might want to talk to the companies directly, not a salesman in a third-party storefront.