Well I was focussing on the EMC directive/regulation and this statement:
The regulations require that all electrical and electronic apparatus marketed in the UK, including imports, satisfy the requirements of the EMC Directive. The regulations implement a separate regime for fixed installations.
Because you have an RF transmitter and so the EMC must apply. If your module was CE approved, then my guess is you would not require to undertake an assessment, it's a bit like the external PSU path many suppliers chose when they had to prove electrical safety, they just passed the responsibility to the PSU manufacturer.
Battery power or PSU powered, the regulations are the same, basically is the 10mW going to interfere with any other user of the RF bands, is it on frequency and is the transmitted harmonic content below the regulatory requirement. All this (of course) only comes into effect when selling/marketing a product, for home use, whilst the regulations still applies, Ofcom would probably not enforce regulations unless it could be proved the equipment caused interference. Ofcom do regularly prosecute individuals in the amateur radio world, so it is a real world problem to consider and similarly when a device interferes with a Amateur band (433Mhz either on a primary or secondary use basis) they will act to find the source and take measures to control it, again a well published and frequent event.
Your device is well within:
http://stakeholders.ofcom.org.uk/spectrum/information/licence-exempt-radio-use/licence-exempt-devices/short-range-devices-information
SO there is no licence requirement, but type assessment with evidence does unfortunately still appear to be a requirement. For self-assessment purposes, my view is providing you have evidence of design and of your RF module and all associated design documentation and data sheets, then that should be adequate evidence to hold for assurance purposes.
Plus:
The following principles shall be carried out when CE Marking take place by Self Certification:
•The manufacturer, his authorised representative or the importer (economic operator) must ensure and declare that the products meet the essential requirements of applicable directives;
•The economic operator shall establish the technical documentation (Technical File) and keep it for at least ten years after the last product is available for inspection by the competent national authorities
•Based on the TF, the economic operator must be able to demonstrate whether the product complies with the essential requirements of the applicable directive (s). When applicable, the Technical File also covers the design, manufacture and operation of the product
•The economic operator shall take all necessary measures, to ensure that the products are manufactured in accordance with manufacturing process as drawn up in the Technical File and with the essential requirements of the Directive (s) related to the product.
On balance I think self-assessment is viable.