You can request an EHCP directly through the LEA on your local website and bypass preschool, and it will force preschools hand.
EHCPs are an absolute pain in the arse, and the sooner you get it started the sooner you'll be closer to getting an answer.
My own LO was significantly delayed, and nursery were rubbish about getting some support in place, and promised me they'd start the EHCP process and they didn't.
However, when my son started reception they were on the ball. They had more resources, a hands on SENCO, and EHCPs do not require a diagnosis, they simply cater to need.
If your twins do end up in reception before the process is underway, what they will likely do is 3 expedited Assess, Plan, Do reviews. The SENCO will also try and get hold of an Ed Psych, which is incredibly difficult but often necessary. It feels like they never talk about your children's strengths, and only their weaknesses, and it can be tempting to list their strengths at large but this can also often delay necessary support once it's documented on paper.
It is important to know you can actually pay for a private Ed Psych evaluation too.
Hearing tests are usually pretty quick to turn around, and IME SALT can also be pretty quick too, but you can also pay privately and use private SALT reports to support an EHCP, even though the LEA will try and tell you you can't. You can, and if they say otherwise you can remind them it is lawful to do so.
Preschool will probably suggest the early help programme which will involve the health visitor and hopefully speech and language, and they can get the ball rolling for you.
What I will say is, make a decision now about whether your preferred setting is mainstream or specialist. If you think specialist will be better overall, it is best to put your foot in the door now.
I would say our LEA are quite fast, but DS is 6, has resat reception twice, and has only just got specialist provision approved, with no named placement yet so will be going back to mainstream in September. He will probably be 7 before he even gets into specialist, so I wish I'd been firmer, dug my elbows in, and had the school back me up that they don't have the resources for unlimited interventions. This is obviously just my experience and what you want to try is completely up to you, but I think it's important that you know this can happen.
Wish you all the best.