SDB73,
I cannot speak to the process in the UK. However, I have started and had approved several Transport Canada approved manufacturers - though not for avionics. I would expect that like Canada, in the UK, it's probably something like: When you know that you have what it takes to do it, and can demonstrate it, you probably can be approved to do it.
I don't say this to be exclusive, it's more like the old saying, if you have to ask "how much?", you probably cannot afford it. I know that generally, the regulators, despite their desire to assist, don't have the time or mandate to lead applicants through the process. You have to present an application and proposal which is pretty well compliant going in the door.
Consider that (using the Canadian model) you have regulatory approval of both the new design (probably by TSO or STC), and the company itself who will produce and certify it. These are two very distinct activities, and probably must happen concurrently for the first product.
Some of the standards which might prevail over avionics will be found here:
Index to RTCA Documents
Others will be found in the "Part.23" series of the FAA FARs, or your national equivalent (assuming that you're talking light fixed wing aircraft). Available here:
RGL Home
The Canadian standards for approving an aviation manufacturer (irrespective of product type) are here, just for your reference:
(read this, and the associated standard linked at the top)
Part V - Airworthiness - Transport Canada