Completely common, sadly.
They can't refuse to assess because of no dx. It break the SEN Code of Practice, which categorically states that Statementing should focus on need, not dx.
J was Statemented at 3, just before he started school, after a year long fight. He had no dx except a possible ADHD, but was at nursery full-time, who provided a mass of info, but we were turned down for assessment, despite the nursery saying he needed full time 1:1 for safety reasons (climbing, hitting, biting, running off, hitting kids/ adults with knives and scissors). The reason? Didn't meet criteria. Which criteria? They wouldn't say!
We then appealed and wrote to our MP. They agreed to assess, and we withdrew our appeal. They Statemented him and he got about 23 hours, which the school topped up to full-time from their own funds.
The unsafe behaviour carried on at school and worsened. We and the school repeatedly requested full-time funding. The LEA refused. J was dx'd with ADHD. They still refused (rightly, I guess, as his needs were no different just because of a dx - but not rightly, as he should have had full time in the first place!)
The unsafe behaviour continued into Year 1 and Year 2. He got dx'd autism as well at this point.
We appealed to SENDIST and wrote to our MP...cue big backtrack and 33 hours of 1:1 support.
You have to evidence EVERYTHING. The key words are safety of self and others. You have to write to everyone who can help - our MP was fantastic, and you have to get your SENDIST appeal started.
Think of the refusal like a screening technique. They say no to (virtually) everyone and then that saves them money, as only the ones who care enough or know enough will push for something to happen.
Good luck - be one of the ones who pushes. My J wouldn't be in school any more without his Statement.