Probably the GWML between Oxford/Reading to Paddington.
Most overbridges on the route appear to have a particularily high clearance (work has also been undertaken recently to improve clearance where appropriate for larger containers).
That sounds about right going on my knowlege of the GWML. As far as I recall, Brunel originally built the line to 7ft (wide) gauge, which implicitly gave a much more generous loading gauge than what could be found on the SR lines around London.
I don't know if Brunels' wide gauge was nearly generous enough to accommodate an EU style double-deck train...But if it is, that might suggest it'd be possible to run double-deck services between London and Penzance, and possibly between Bristol and Swansea as well. 8)
Class 166 units are said to have been built to a particularily generous width thus limiting their use to the GWML, thus a precedent has been set for using stock restricted to this route.
I can verify that Class 166s are also used on the North Downs line running RDG > WKM > GLD > GTW as I used to commute daily between Blackwater and Guildford.
Although I'd guess (Thinking of many old structures on and near the route) that the line might've been built to standard gauge as opposed to Brunellian wide...But if the latter is the case, it might also allow double-deck Guildford/Gatwick flyers - Assuming that the Guildford tunnel was built as part of the North Downs route.
As the line has a lot of short platforms (BAW
only just accommodates a three-car 165!) it could prove
very useful during morning peak services in both directions. We all know that Reading is a constant bottleneck, but the 07:58 and 08:21s from BAW to GLD are always crammed to the rafters with pupils commuting to the two popular prep schools along the route as well!

hock:
Of course there are the problems with doubledecker trains... higher dwell times, difficulty in checking tickets, limitation of luggage racks, etc.
My experience of double-deck trains is limited to a handful of runs on German DBAG and Finnish VR services...But from what I remember, dwell time on these services hasn't been any greater than what an 8-car 450 often requires. Indeed, the German DD services that I've used between Hamburg and Bremen get a minute per call...But often manage to load/offload completely within 30-45 seconds! 8)