I have the same problem not being allowed expanding ammunition as I don't have provision to use it on live quarry in this country. My local force so far have not budged from the chart in the home office guidance which states .375 is only for dangerous game. Even though I can shoot reds with my other rifles.
However, I found the following in the HO guidance notes which I will be putting to them in due course
13.35 The police will wish to be satisfied that
an applicant has genuine intentions to use
such rifles abroad, though such visits may be
infrequent. Due to the terms of section 9 of
the 1997 Act, expanding ammunition may not
be authorised in connection with use abroad.
Zeroing with non-expanding ammunition may
be permitted in the UK providing a suitable
range or land is available. Those who homeload
their non-expanding ammunition for
such zeroing will also need to test and
chronograph it. Some rifles intended for
antelope and other Plains Game may also
be suitable for deer, boar or other quarry
shooting in this country. Calibres such as
the .375 (9.5mm) are at the lower end of
those suitable for shooting “dangerous game”
but may, once initial “good reason” has been
established, also be used for shooting the
larger deer species in Britain. Expanding
ammunition may also be authorised for an
applicant whose certificate allows for the rifle
also to be used for shooting deer in Britain.
Where a shooter experiences difficulties in
obtaining “dangerous game” cartridges in the
country where that game is to be hunted,
arrangements can be made for a dealer to
export an appropriate quantity which can
be collected by the shooter at the point
of embarkation.