I have heard of a similar case recently - you want to get on the phone to the vat helpline immediately and specifically flag this up as fraud (ie not your doing) and make clear you need written confirmation from them that thay have this fact noted on their file and they will not bother you again ref tis vat number unless it is to take necessary steps to cahnjcel registration process.
You should get name of officer you speak to and call reference and request written confirmation as matter of urgency.
Personally i would request copies of all inromation that was used on application to help you ascertain if your perosnal details have been compromised - i think from the case we came across the proof of personage provided clearly did not come from our client.
Knowing hmrc they may be relucant to provide you with info linked to your record - if they won't provide specific information demand that they liaise with you so they can confrim if information does match proepr information that you hold on file - eg if you supplied relevant info they might confirm what they held on file matches or not - they should be able to get a nadle on whether your info has ben compromised but i suspect they might be reluctant to tell you if it has or not.
Also it seems clear your gateway has been hacked - so you need to contact online services to do similar to get that gateway account terminated immediately.
I would finally specfically ask them to check what other recent activity has gone on via gateway or account so you don't find out in say 12 months time that a cis refund or something simlar has been actioned via your gateway.
Hopefully hmrc take such fraudulent activity seriously but i don't know how thorough they are if i am being honest if all your id's have been compromised.
If you have the slightest suspision your email account may have been hacked - you should change all your email passwords as approrpiate.