Yes, no LLU means the cheapest deals usually vanish e.g. the TV adverts for Sky and TalkTalk don't apply.
Also some providers will charge more in your location e.g. PlusNet and EE.
Sky will offer to connect you, but at £17 per month and it is a product to avoid due to congestion issues.
BT Retail can be a reasonable choice if you find Primus are unwilling to connect you once the move has completed. Ordering another broadband service while the phone line is being installed will be very difficult.
The question is whether you keep the line rental with Primus, as providers are trying to force bundles on people these days.
PlusNet works out around £19.49 per month for unlimited broadband, and reflects the costs of providing unlimited on this exchange, i.e. you can get an idea why Primus may be reluctant to connect you.
There is a chance that once you have moved the phone line, Primus will still happily connect your broadband at their low prices,