Yes this has been done recently, something to do with gauge clearance on Hamble Bridge?
So having had a quick look at the Sectional Appendix,
The Cl.43s have an 'OPPOS' restriction between Laverstock South Jn and Salisbury Tunnel Jn;
A 'Not Permitted' between St Deny's Jn - Change of LOR (where every other diesel locomotive class has a blanket 15mph restriction. This would be over Hamble viaduct.
OPPOS applies between Laverstock South Jn and Salisbury Tunnel Jn
15 mph over Hamble viaduct No.29 (8m 75ch) between Burlesdon and Swanwick
With regard to the coaching stock - only the un-modded Mark III stock has clearance (one presumes, currently) which also, currently, excludes the Mark III DVT which doesn't have clearance.
OPPOS -
Running lines or sidings mentioned on the right hand side of the load looking in the
direction of travel must be clear and no train signalled 2-6-2 or 2-6-3 must be allowed on
the running lines or sidings on the left hand side of the load. To be signalled by the
special is line clear 2-6-3
So I would foresee a little bit of work being required to allow an HST in any description to run that particular route.