Where can you get an ATA/TIR carnet stamped?

Some of the Inland Border Facilities can stamp ATA Carnets, and can be the Office of Departure for transit movements.

You should tell HMRC in advance that you’re attending an inland border facility if the goods you’re moving:

are going to an office of departure or office of destination (starting or ending a transit movement)
are covered by an ATA Carnet

https://www.gov.uk/government/publications/attending-an-inland-border-facility/attending-an-inland-border-facility#locations-of-inland-border-facilities-listed-north-to-south

What is a CMR?

A road consignment (CMR) note is a standard contract used by companies who want to use a provider to transport goods internationally by road.

The CMR note confirms that the haulage company has received the goods and has a contract from the supplier to carry them.

You must have a CMR note on all international journeys if you’re carrying goods on a commercial basis.

The CMR note can be filled in by either:

you (the haulier)
the company sending the goods abroad
a freight forwarder

You will need 3 copies of a CMR note, including one:

for the supplier of the goods
for the eventual customer
to accompany the goods while they are being transported
Sample of CMR document.

You can buy pre-printed CMR notes from the Road Haulage Association (RHA) and Logistics UK.

https://www.gov.uk/guidance/carry-out-international-road-haulage#complete-a-road-consignment-cmr-note
https://unece.org/fileadmin/DAM/trans/conventn/cmr_e.pdf

What documentation do you need for fresh water fish?

They’ll need an Export Health Certificate and all the customs paper work.

But they don’t need a catch certificate.

In addition to the export health certificate as appropriate for the product/live aquatic animal being transported, if they are transporting live fish, then they will have to meet the welfare in transport rules, and if these hauliers are GB registered, then, unless it is specifically covered in the agreement between the EU and the UK (and it is unclear if it is), they will require:

  1. a transporter authorisation,
  2. a certificate of approval for the vehicle and
  3. the operator will have to have a certificate of competence issued by an EU member state.

Details (from the EU web portal) are here: https://ec.europa.eu/info/sites/default/files/file_import/animal_transport_en.pdf