Hopefully this will be of help!
As the posts above, it is possible to meet Part L standards without undertaking the thermal bridging calculations, but it is challenging and would need very efficient building fabric to compensate.
You do not need to be qualified or accredited to undertake the thermal bridging calculations. Anyone can undertake them, similar to producing U-value calculations, however there are 'modelling conventions' you have to follow to ensure the thermal bridging (psi-value) results are accurate, these are detailed in BR497. As a side note, the modelling conventions for producing U-value calculations are detailed in BR443.
THERM is free software which can be used to calculate psi-values; it's not the easiest tool to use, but it's more than capable. A link to download the software is below:
THERM Software Downloads | Windows & Daylighting
If your building is simple masonry construction, you may be able to use psi-values from the Recognised Construction Details website, a link to this is below:
https://www.recognisedconstructiondetails.co.uk/
