There is a facility called "Simultaneous Provide". Not many ISPs do it, and even fewer have frontline staff who know about it.
Can you tell for sure what exchange the new flat is on? The safest way is to put its existing telephone number into this checker
. Post the link to the result. If not, on that same site there is an Exchange Mapping page. You can drill down to the address from that, but not 100% guaranteed accurate.
If you want to go for a simultaneous provide you have to make that clear at the time you order the phone, but broadband doesn't have to be from the same suppplier. The phone company should then be able to give you a "Linked Order Number".
It would be easiest now if you give us that link, as that will tell us which ISPs you can get. Otherwise there are too many possibilities to discuss.
My broadband basic info/help site - www.robertos.me.uk
My domains,website and mail hosting - Tsohost
. Internet connection -