Ignore 99% of the replies you are going to get and seek legal advice ASAP. Are you a member of any organisations like BASC, BDS, NGO.... speak to them
legal advice via a solicitor will be expensive, agree with your second part if a member of a shooting organisation.
However will give you my 1% from experience of being a club secretary for many years.
The police are very risk adverse ie they will always remove any risk of firearms being used if certain allegations are made.
if you voluntarily allow the removal of the firearms whilst pending investigation, then there is no legal time constraints on the police on how long that may take, many months even years is not untypical.
If they revoke you do have a legal time constraints in which to appeal.
putting the firearms in storage, will remove the potential harm, may also help if it can be shown they were in storage at the time the neighbour made an allegation that you threatened them by pointing your gun at them.
However if in storage they can still revoke your certificate as all the time you have your certificate you can get the firearms out of storage, Once revoked your guns could remain in storage for a very long time, during the legal appeal process.
Two real life examples, one very similar to yours, neighbour made allegation of firearms owners making threatening behaviour that escalated to involving the police. firearms were removed and certificate originally voluntarily surrender.
After many months the advice given to the certificate holder was if he wanted his guns back quick was to move house, so conflict no longer possible. He surrendered permanently his certificate, deciding the costs of moving or reapplying after five years as was also suggested and then possibly still having to appealing were not practical.
He did arrange for one of his shotguns to go on a friend’s certificate and continues to shoot clay pigeons accompanied by his friend at clay grounds with a a section 11(6) exemption.
The other was an argument with a neighbour over parking his car such that he blocked the certificate owners driveway, words were exchanged and the certificate owner thought no more of it, until that evening armed police arrived to remove his firearms as allegations made he had threatened the neighbour that day.
Fortunately the words exchange between the two was all recorded on the certificate holders CCTV which clearly showed no threat had been made just a polite request not to obstruct the driveway. His firearms were not taken and the neighbour got a visit from the police.
If it’s been going on for three years is there no way of reconciling the situation with your neighbour?