I am not going to dox myself, but I have in a past life had some responsibility for alcohol licences. You need to get advice because this was 10 years ago, but I do not think the relevant statues have altered significantly. It is not down to the police to grant a licence. They are one of the "responsible bodies" and they can object, but they are not the ones who are responsible for granting licences. That is the local authority and their licencing committee. It was not uncommon that we granted licences that the police objected to but obviously their claims had to be considered seriously.
The responsible bodies are:
local fire and rescue
primary care trust (PCT) or local health board (LHB)primary care trust (PCT) or local health board (LHB)
the relevant licensing authority
local enforcement agency for the Health and Safety at Work etc Act 1974
environmental health authority
body responsible for the protection of children from harm
local trading standards
any other licensing authority in whose area part of the premises is situated
Home Office Immigration Enforcement (on behalf of the Secretary of State)
This is the relevant section on the current .gov.uk website (hence why I believe it is still the same process).
If representations are made by a responsible authority or other person, it is for the licensing authority to decide whether those representations are relevant to the licensing objectives and not frivolous or vexatious. If the licensing authority decides that any representations are relevant, then it must hold a hearing to consider them.
If you can, speak to a local licencee to see if they had a local solicitor or licencing consultant, they might give you a pointer in who to ask for help.